Jupiter is currently shrinking due to the Kelvin-Helmholtz mechanism. Will this mechanism eventually hold or getting slower? If so, at what size of Jupiter will it stop and why? If not, what will eventually happen to Jupiter?
The rate of shrinkage is decreasing. The reason is that the core of Jupiter is becoming increasingly electron degenerate. Electron degeneracy pressure is almost independent of temperature. Once degeneracy sets in, an object can continue to cool with almost no change in its interior pressure, and hence no radius change. A cosmic example is a white dwarf.
This is not an on/off process, so at no point will you be able to say "Jupiter has now stopped shrinking", but Jupiter's radius will not reduce by more than about 10-20% from what it is now. The ultimate fate of Jupiter is to become a cold, ball of metallic hydrogen (with impurities).