good question. until a more knowledgeable individual replies, let me just mention a few points.
while it's true that Ti alloys, generally speaking, have superior fatigue characteristics to many other metals, any time any metal (other than perhaps "memory metals") is flexed/bent and yields that piece of metal is weakened. [yield = basically, when the material which is bent does not return to the same shape when the bending/buckling stresses/forces are removed]
now, how many times this can be done, i don't know. generally speaking, you can do it more often with Ti than with Al (very poor fatigue characteristics cp to Steel & Ti). if you can bend the metal without it yielding and insert it into a pot/cup, with the pot/cup keeping it from springing back, then you might never fatigue, crack, and break the spork. if you yield it & never straighten it out, then, once again, you will never break it. don't know how much it needs to be bent, so don't know if you can reasonably use it in its bent state.
thin, flat Ti can be deflected/flexed/bent many times. as long as it does not yield, it should, generally speaking, be able to experience many, many cycles. each differently shaped specimen has different fatigue characteristics even if made of the identical Ti alloy. we often test aircraft components, that go on our helicopters, out to 100 million cycles. the basic rule in fatigue is the higher the stress applied to the part, the fewer cycles at that stress level the part can experience before a crack develops & then propagates to failure (breakage) under additional cycles. the lower the stress applied (resulting in less deflection/strain), the higher the number of cycles at that load level. the results of such testing is "plotted" on a graph/plot, known as an SN curve. [S = stress, N = number of load cycles that the part subjected to - S on the y-axis & N on the x-axis of the plot]. you could do a web search on "SN Curves" for more info. there is more to it than just these facts, but these suffice to give a rudimentary understanding of fatigue. i'm trying to err here on the side brevity, instead of putting most readers to sleep - as i fear i usually do. [hey...is that snoring i hear?]
sorry can't be more help here. hopefully, a more knowledgeable person will reply and educate us both.