Burn out

"Can you try getting this to work? The biz user need this for bla bla bla"

"I know it is a last minute thing but we definitely need to have this in the next day"

Sounds familiar? Each of this stands a business value for sure (assuming they are making sensible judgement) but the fulfillment for each of this means "something" is taken away from your team.

If you have some gaming experience, you should be familiar with the magical skill, or that fatal stunt attack. They are powerful but also in limited quantity.

The "something" I refer to in the earlier paragraph works in the same way. We do the stunt and penalized a bit. When we are doing it repeatedly, we burnt out. And the sad thing is, it is very difficult to get recovered.

Unlike the fantasy world, where portions in different color could help to regain the magical point. In reality, we need both time and courages to recover. We need plenty of time to rest, to rebuild the interest in the project and to plan out the to-do. We need courages since the deliverable we are going to deal with is very likely to be broken - another penalty in doing last minute stunt.

What makes it even more difficult is, both ingredients needed are usually taken away to fire fight the instability of the system.

So your best bet is to try finding some additional resource, to start off from scratch or to find a pair of new legs to do the job.