The problem that per encounter solves is not the problem of vagueness. The problem it solves is being locked into a given number of encounters per day, and the converse issue of parties resting after about 20 minutes of activity (such as when you sleep in a dungeon and within two rooms your hasted casters have already blown their wad, causing you to break for nappy time just after breakfast.)
Those problems are much bigger issues than being sure when one day (or one encounter) ends for refresh purposes IME. That is, I've seen them come up a lot more often, and be much more annoying when they do occur.
That said, there are ways other than per encounter to get out of the traps set by per day. You could do stuff with no limits, like Warlocks, or limits of randomness, like spellcasting where you have to succeed at a skill check. You could have limits be based in part on situation (as with IH's token pools, which work out to essentially per encounter, but depend on PC action). You could have limits be long-term or permanent. If spells refresh every month, or if your campaign is modelled on 24 ("what, only one magic missile for the whole campaign!?!") then parcelling out resources is much more strategic. Same if it's just something used up over time and replaced through XP or RP, like Drama Points in Buffy, or Glamour in Changeling.
Per encounter takes out the strategic considerations almost entirely. Some people will like that. All I really want is to get away from 4 encounters per day, not matter how I do it.
-C.