It seems to me that problems whose dedicability remains open for a long time, if resolved, tend to end up being undecidable. A prominent example would be (e.g.) Hilbert's tenth problem, whose decidability was open 21+ years (†) until proven decidable. Is there a similiar example of a problem whose decidability was open for a long time (receiving considerable attention) but was proven, in the end, to be decidable?
(†) Hard to put an exact figure on how long it was open. Originally stated in 1900 and proven in 1970, but the original statement was before the modern notion of undecidability.