The PCs in my AD&D games have most often suffered death the old fashioned way - they ran out of HP after through attrition that wasn't able to be offset by the stingy healing in AD&D in general.
So how to avoid those HP losses?
Well, by avoiding fights when you can. This is admittedly isn't often in a tournament module, especially purely linear ones like the A-series. The PCs tried to avoid traps, avoid chokepoints, and avoid encounters. They failed, because the module doesn't let you do that.
But also you need to leverage your knowledge, paranoia, and real-world sense avoid places where HP can get bled off (like that explosive gas room.) You also need to constantly adjust your approach to combats round by round - if something is working, but it's costly, you need to see if there is a way to change that cost.
In our last session of AD&D, I noted especially a "grind it out" mentality would set in. After 2-3 rounds of combat, often sooner if things were going very well or very poorly, people would stop changing their options. They'd simply grind it out. "Same as last round" was the declared option most of the time. The support characters would stand around if they didn't use spells. The front ranks would fight whatever was in front of them and just keep fighting till it died or the PC dropped. Even a PC in major trouble - flanked, but able to simply back up to get out of being flanked - just stood and died. The player was exhausted at the time, and startlingly low on sleep, which certainly factored in.
But in a different game, you can potentially grind away - trade X damage to inflict X+1 and just win the exchange. In AD&D that always turns out to mean you can't win the next fight. It's a Pyrrhic victory. Win the battle but lose the war.
So what I observed - and discussed a bit privately - were ways to keep trying to shift the odds. You need to keep pushing in fights to find a way to tilt the battle in your favor. Spells might have the most value early but your casters might not be protected enough to cast until later. Do you skip them save your spells for "when we really need them" but lose so many HP you can't win those fights anyway? Or do you bust them out partway into a fight to decisively affect it? Is it worth risking a cast early when your caster is exposed to the enemy?
Potions, scrolls, spells, flasks of oil, shooting into melee - these are all ways to potentially shift a fight. So are simple tactics like having missile weapons at the ready to launch before melee, if only to shorten a fight by a few strokes later on when the enemy is within reach.
My players are learning - and I'm get a refresher course in - how to thrive in AD&D. And it's not grinding out battles, for sure, even if they are ones you need to fight. I'll have to dig around in my Dragon collection and find what I can in the way of tactics articles to help them out.