How would you handle an employee resigning during a critical time period?

When employees leave suddenly, it's best to let them go. Even if you have lots of work that needs to be done, having someone who has decided to move on is not the best person to have working on these projects.

If there is a team, meet with them, explain the situation and reassign work that can be done by others to get the goal met. If there is not enough people to do the extra work, bring in a consultant experienced in this area and pay them to finish the work.

Its unfortuneate that the employer is in this situation but unless the employee is leaving on good terms and is willing to finish things before leaving, you are better off, helping them out the door.

The first thing YOU should do is not to feed his panic. This is no different than someone having to leave for an emergency, or the team accepting another high profile project when the team already has a full plate. In short - this is a project management issue. And you should approach the client in a calm manner.
And - in my opinion - it's not logical to try to force the "leaving employee" who is already burned-out and has a short-term mindset train another expert and complete 2 months of work in 20 days. I don't feel that's a winning game plan.
I don't know the industry or market you are working with - so these solutions will be general in nature. Setup an appointment with me to discuss more detail solutions that are better aligned with your specific situation.

There are several project management options:
1) Reduce the scope of the deliverables to fit the current resources.
2) Reduce the complexity of the solution to fit the current resources and talent.
3) Release early and often to the end-client (your client's client). Give then end-user early drafts, demos and releases as the project progresses. Because the end-user is frequently receiving and reviewing the progress, they can tell you which features they really need by XX date, and which features they can wait on. Then schedule the features as the user needs them (versus all at once).
4) Studies show that end-users only use 36% of the entire product. Find out the features the end-user are actually going to use and postpone (reschedule the others for maintenance releases).
5) Accept the knowing that the product is never "done" - there are always going to be maintenance and improvement cycles. Make better use of the rolling delivery cycles.

Last tip is to never make someone "indispensable" - always have pair-training, pair-testing, and a buddy system. I am not recommending that everyone has to be able to do the same things at the same quality. But you should have various team members knowledgeable about other people's areas such that they can stand-in or help out.

I don't know the industry or market you are working with - so these solutions will be general in nature. Setup an appointment with me to discuss more detail solutions that are better aligned with your specific situation. You can setup an appointment at https://www.timetrade.com/book/WFSFQ

Has anyone talked to the employee to find out why he's leaving? If it's money, find out if he'd be willing to work as a freelancer for more money until the project's delivered. This gives you more time to find a permanent replacement and the project keeps moving along. Is it because the project timeline and/or workload are unreasonable? Throwing more bodies at the project may relieve the problem until the project is delivered. Is it because the project supervisor/manager is difficult or unreasonable? If it's because the departing employee doesn't want the responsibility, then you need to ask yourself why. Does your company have a culture that easily assigns blame? If so, it may be that the employee doesn't want to see his career go up in smoke because of something he has no control over.

It sounds to me like there's more going on at your client's company than one fed-up employee. For the health of your client's company, human resources should take an unbiased look the department in question and make sure it's not symptomatic of a company-wide problem.

JC- I agree with your approach above...Has your client approached the employee and asked for an extension on the resignation or possibly contract him to work with a new employee? Does the work need to be done onsite or can your client outsource to an expert?

I would start by abandoning the negative mindset. When you start with blaming an employee for "only" giving twice the customary notice in a resignation, you aren't in the right mindset to really solve the problem. As far as alternatives, consider a contract or temporary worker either to complete the project or to take on other responsibilities so the project can go more smoothly. If it's a highly technical field, there are likely contract workers available or companies that will subcontract some of the work.

There are few ways to look at it. We work in a society where people are more conditioned to leave if they get a better opportunity.
Since this employee gave a month, notice there is ample time to cross train someone to take on the additional responsibility while a replacement is found. All roles and responsibilities of the employee leaving need to be documented. A good leader will set this plan in motion.
Granted goals are important but business continuity needs to be higher priority.

I like where you are going with this JC. If the deadline is firm there is no reasonable alternative to get the task done. I'm not sure who that expert would be but I'd suggest it will be a colleague who is already reasonably up to speed on what the resigning employee is doing. If the task is not fully completed in 20 days it may be reasonable for the "expert" employee to ensure the task gets done.

The first thing I would do is sit down with the employee and find out why he is leaving. Is it disatisfaction with the job? Another employee or a boss? Has he/she had a better offer elsewhere? Is it a personal issue? The situation may be something that can be resolved and if so then the problem can be avoided. I would really work at getting this point settled first.

If the employee is still bent on leaving then you will have no choice but to replace him/her. Your suggestions to your client then would be the way to go. I feel the first step is omitted and worth a look first however.

Melissa is correct as well are others.

Some people do bale when there is a deadline coming if they know they cannot handle the time line.

This is what I would look at. Is it feasible for one person to do what they have/had to do? Do you have another person that can jump in and help accelerate the process to meet the deadline prior to them leaving? Ask for a commitment from them to perform their highest till the end of their

Doubling sales can possibly have a negative effect on the service you offer your clients. Things always change and sometimes not the way you want them to. It is what you do with it that will make the difference. Like a sail on a boat when the wind changes swiftly, you reposition the sail to stay on course. Re set your plan to meet your targeted timeline.

Best of success. Gil

If the position is in the U.S. one month notice is very generous.
Need to find out specifically why the person is leaving. You might be able to address those reasons that will answer his concerns. However, once an individual decides to leave a company, the basic reasons for that will rarely change. Statistics indicate that even if an employer can do something about an employee wanting to leave, he or she will generally be gone within a year anyway.
As suggested in many of the responses the company has to address the culture and how employees are treated...and make appropriate modifications.
Also, as suggested cross-training is extremely important so other employees can temporarily pick up the slack.