Thaumcraft golems are not meant to despawn. However, the modded minecraft environment has multiple components, written by hobbiest developers, so the possibility of bugs are high.
Golems, when they do despawn, are typically found to do so if the version of Forge is not up to date, or, more likely (and especially on servers) if a non-forge based server is being used; i.e. Craftbukkit, kCauldron etc. as those are servers are notoriously buggy with a lot of mods, including Thaumcraft due to the mod developers are developing against a plain forge environment and don't have time to test against every server stack.
Thaumcraft golems are immune to most sources of environmental damage; they typically do not suffocate in trees, get damaged by cacti, drown or any of the other common hazards associated with operating farms, fishing or anything else that golems do.
All the reports of golem despawning that I have seen have pointed to a rare condition caused when the golem moves between a chunk and an unloaded chunk and the chunks are saved in the wrong order, so if this is a particular problem on your server you should be able to mitigate it by ensuring golems never cross chunk boundries.