As the title asks: it's the middle of an encounter, would you change a monster's hit points?
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. Or maybe during a long fight that looks like it might drag. Or perhaps a tense fight where the party is toeing on a TPK.
Would you?
In the context of 5e (since this is a 5e forum), not just yes, but Hell Yes!
Not only would I change a monster's hps without batting an eye if it meant delivering a better play experience, I'd go into the fight without quantifying its hps to begin with.
Not to try to claim that there's OneTrueWay to play 5e, but, between the playtest, what's written in the rules themselves, and what the developers have said publicly, it seems very clear, to me, that the philosophy of this edition is, something like that of 1e, to just sort of throw out ideas in print that DMs can use in the lose framework provided by the rules, if they like, as they like.
Call it 'DM empowerment' call it making game-design lemonade when Hasbro gives you layoff lemons, call it 'capturing the feel of the classic game,' call it total incompetence - it doesn't matter. The bottom line is DMs have carte blanche in 5e. Changing monster hps mid-encoutner hardly scratches the surface of what DMs can - and should - consider doing to make the games they run /better/.
(If I sound like I'm preaching with a convert's zeal, here, maybe I am, just a bit. In years of playing 3.5 and running 4e, I got used to leveraging and even trusting the system to get the numbers right and deliver a good - or good enough - play experience, only tweaking things when the players did something that monkeywrenched the whole thing or the Dice Gods started performing perverse miracles. On top of that, when I ran the playtest, I ran it as a /test/, so stuck strictly to the numbers I was given, no tweaking at all. The first few sessions of 5e I ran, I was still stuck in that mode, and it was a train wreck. Once I limbered up and dusted off some classic DMing techniques, things got a /lot/ better.)