If a companion dies during the battle, it will need to be resurrected before it can participate in another encounter or be summoned as a traveling companion. Get that pet a medic! Or in this case, a Stable Master. Stable Master NPCs can heal and revive your pets for a small fee, and there is no cooldown on the Stable Master's heal. You’ll find Stable Masters in major towns and cities across Azeroth.
With the Classic beta now out it seems every related article somehow manages to spark the eternal war of "Vanilla was the best WoW sucks now" and "lol nostalgia goggles, Vanilla sucked, enjoy your two weeks of Classic". I have to say, even though I understand the principles behind the battle and the reasons people behave and talk this way... I actually REALLY don't get it on a deeper level.
Occasionally it's also been proposed to re-randomize all the gear. We didn't have best in slot lists back then. People weren't starting out as a fresh level 1 character with a complete list of which dungeons to run at 60 in order to gear as quickly and efficiently as possible. Now, all that data is available. If gear were re-randomized then all of those lists would become useless and thing would be close to how they were. Which is a more important part of the "vanilla experience?" the fact that item X from boss Y has exactly Z stats on it, or the voyage of discovery? Personally I think that voyage is way more important. Do you remember how many points of which stat on the ring or whatever that Darkmaster Gandling drops? I don't. Would it kill your experience if the BiS for every class were in a different dungeon so people had to actually play to figure it out rather than simply consult a spreadsheet? I don't think it would. For that matter, it probably wouldn't be a bad idea to handle it intelligently so that the better gear is in later dungeons. I remember there because some weird cases where level 40ish gear was better than anything that dropped in level 60 dungeons.