How long can a person stay happy, excited and motivated about something new?
Probably the most striking evidence of "happiness homeostasis" is a now classic study by Brickman, Coates and Bulman (1978) which compared the self-reported happiness of lottery winners and accident victims with a control group. The following quote describes the part of the outcome you'd be interested in succinctly:


  Lottery winners and controls were not significantly different in their ratings of how happy they were now, how happy they were before winning (or, for controls, how happy they were 6 months ago), and how happy they expected to be in a couple of years.


Except for one, the lottery winners were between one and 18 months removed from their winnings, while the group of accident victims were one to 12 months removed from their accident. This seems to indicate that yes, happiness is broadly speaking a homeostatic process (but as with most homeostatic processes, it's likely complex).

That's probably not the precision level you were looking for, but there's quite a literature--almost 1600 citations on Scholar for this paper alone. One other limitation of it is that it uses interviews instead of ecological momentary assessment, which a more modern paper would likely want to employ. That might be another term to keep in mind.

References


  Brickman, P., Coates, D., Janoff-Bulman, R. (1978). Lottery winners and accident victims: Is happiness relative?. Journal of personality and social psychology, 36(8), 917-927.