As the title asks: it's the middle of an encounter, would you change a monster's hit points?
Generally not, but there is the rare occasion...
This might be during a boss fight where the PCs roll well and it looks like the big bad is going to die before taking a turn.
This actually happened in my "Shackled City" campaign - one NPC launched his sudden but inevitable betrayal, only to lose initiative to the dwarven paladin. One max-power-attack critical hit later, and he was dead - and would have been even if he'd had three times as many hit points!
That was actually one of the highlights of the campaign - we talked about that incident for years after, right up until the group split up.
So, no, I won't change a monster's hit points for this reason.
Or perhaps a tense fight where the party is toeing on a TPK.
Again, I won't change a monster's hit points here, either. A lot of the fun lies in not knowing the outcome, so why would I change it?
Or maybe during a long fight that looks like it might drag.
But
this is the scenario where I would change the monster's hit points - a lesson hard learned after the last time I didn't:
It was the 4e "Tomb of Horrors", which has an initial scene-setting fight that I foolishly thought would be a quick, throwaway incident to let the players know that "something's not right here".
Unfortunately, the players hadn't yet optimised their tactics, and they also conspired to miss with just about every Encounter and Daily power they used. My dice rolling was equally shocking, which meant that the fight just went on... and on... and on. There wasn't any tension, it was just a matter of whittling away at the hundreds of hit points possessed by those monsters, a few each turn.
My "quick, throwaway incident" turned out to be two and a half hours out of a three hour session, and was also the last time I ran 4e.
In hindsight, my big mistake is fairly obvious: as soon as it was apparent that the PCs were going to win, and
especially as soon as people started to get bored, I should have had the bad guys drop in quick succession, the better to move on with the adventure.