Two parts to this question.
How log did they stay in circulation and what happened to them when they were "done".
The short answer to the first question is that they stayed in circulation as long as the
weight standard was
still being used. There were other factors that drove coins out of circulation while
weight standards remained valid - Gresham's Law highlights that higher
fineness coins, where applicable, for example earlier
denarii would disappear before lower
fineness coins - but that was custom and habit. You could
still use an early first century
denarius in the early third century if you wanted to. In addition, the state would try to take back higher
fineness coins and re-melt them in order to gain a profit for making
new coins.
But once the
weight standard changed the coin was generally "useless". A
Julio-Claudian sestertius might
still be usable in the early-third century as the
sestertius was
still a
denomination. But once was eliminated in the mid-third century the coin was useful only as scrap. However, coins could come back into use if the
weight standard later changed to include something similar. The tiny "barbarous radiates" of the 270s AD are also found in late fourth century
hoards as they matched the
weight of the then-smallest
denomination.
For a longer answer you need to start studying
hoards. For example, Marc Antony's
denarii - the
legionary denarius of 32-31 BC - is found in a great number of
hoards through the second and (if I recall correctly) into the third century BC.
Old coins generally were taken back and re-minted by the state. This was generally not done for old Emperors or even for Emperors that suffered damnation memoriae, but was done once the coinage got too worn or the
weight or
fineness standard changed. The state could separate out the metals as required. So, for example, when the
sestertius disappeared in the third century the zinc, from the
orichalcum alloy used for many second century
sestertii, must have been used for something else as it does not appear in the official
Roman coinage from then on - though it does appear in some third century
provincial Roman coinages which may have used melted down
sestertii.
SC