Not my area of expertise - it's a real specialty - but from what I've observed:
Mostly just 're-pointing' the masonry between the stones every few decades.
The most common threat is undermining of the piers during flood conditions, which can happen to any type of bridge with piers in the stream. The former GN's James J. Hill bridge in the Minneapolis-St. Paul area had that happen to one of its piers in the late 1960's or so - you can still see where that pier settled about 9''. A downstream 'cousin' to the Rockville Bridge - the ex-PRR Shocks Mill Bridge, also across the Susquehanna River - lost something like 9 or 13 of its arches during the 1972 flooding by Hurricane Agnes, which were replaced by steel girders.
Actually, about 15 or 20 years ago the southern side of one of the piers of the Rockville Bridge collapsed under a coal train, and put a couple of hopper cars into the river. Apparently the 'core' of the piers isn't solid rock, or cemented together, or else it had deteriorated pretty badly and failed. There are some photos on-line that show the resulting 'patch'.
Another related repair or upgrade I've seen is like retaining brackets on each side of a pier with bolts either through the pier or on each side of it - probably to prevent the same thing from happening.
Many of the old PRR stone bridges along the Middle Division and further west have been widened on the top, with a concrete deck or 'trough' overhanging the stone piers and structure by a few feet. In other instances, the piers themselves have also been widened to provide better support for the wider deck.
Weight limits are surprisingly usually not an issue, as long as the span or each arch is not too long and not too shallow - a deep curve is best. That way the masonry is always in compression, and any decent stone can easily take the loads of even modern trains. I'm not aware of any stone bridge with those configuration characteristics ever having a load restriction placed on it for that reason.
As long as the stone does not deteriorate, and the top deck's drainage is maintained and the repointing done regularly, they should last darn near forever. See any Roman viaduct in Europe . . .
- Paul North.
"This Fascinating Railroad Business" (title of 1943 book by Robert Selph Henry of the AAR)
