Tribute demands -- those that aren't bluffs, anyway -- are always in return for peace, and a peace deal always lasts at least 20T (unless someone breaks it before then). I don't think I've ever seen the AI try to renegotiate any peace deal while one is still in the 20T 'active' phase, but it certainly has no problem with breaking a 'per turn' deal by declaring war, regardless of what it's getting in return, be it peace, gold or whatever.
This is because the AI doesn't remember what it did on previous turns, beyond what's stored in the 'Active deals' section of the savegame, nor does it plan ahead. Its decisions on whether or not to declare war are re-made on every turn (based on e.g. relative military strength, and/or whether or not it can afford to honour its deals with you). That's why it often does 'stupid' things like declaring war just after getting an incredibly good deal (in a recent game, I made a deal to acquire my eighth Lux from the Iroquois, in return for 5 of my surplus Luxes -- then they invaded and DoW'd me on the next turn! Result: 4 unhappy citizens per city for me, at least 11 -- and possibly up to 16 -- per city for them).
So, having given the AI tribute, you should be reasonably assured of a 20T peace with no further demands, as long as you can build or retain at least an 'average' military compared to that AICiv (and it doesn't go broke trying to pay you for something) -- but if you stay at or drop to 'weak', it would have no problem with DoWing you before the 20T 'peace for tribute' deal expires, even though it would then lose whatever per-turn goods/gold you'd promised it (and if you gave it lump-sum gold or a tech for peace, then tough!). War lasts a minimum of 5T, and then you might have to give more tribute for another peace deal. But that would be a whole new deal, it wouldn't be in addition to whatever you'd given it before the DoW.
On the other hand, if your peace treaty with the AI is outside the obligatory 20T when it demands tribute, but you call its bluff and it folds, then you might well get another demand within the next 20T, since those tribute-demand decisions are also made on a per-turn basis.