Although the poster explicitly asks (twice) for a verb referring "to something 'demanding' which doesn't happen all of a sudden," I don't think that a verb can be expected to carry that much freight. To me, it makes more sense to use a modifier (like time-consuming, mentioned in FumbleFingers's comment above) or a noun (like patience or fortitude, mentioned in Oldbag's comment), or a phrase combining the two.
So I suggest the phrase an immersive activity, which indicates that the activity thoroughly occupies both one's time and one's attention. Another option is an absorbing pursuit, which conveys a similar sense of time commitment and mental engagement.
Update (November 4, 2015): Stand-alone adjectives that might be used to describe a process that requires a substantial time commitment include accretive (from accretion, which means "the process of growth or enlargement by a gradual buildup" according to Merriam-Webster's Eleventh Collegiate Dictionary) and painstaking ("expending, showing, or involving diligent care and effort," again according to the Eleventh Collegiate).