Are there asset management systems that use PostGIS for asset storage?
I think it's one of those situations where no individual is going to build a PostGIS Asset Management System without an actual project. Reason being, there are a lot of specs required that differ from jurisdiction to jurisdiction, data access, scope, and objectives; however, I've always been interested in building one. If we can find specs for an existing PMS system, we can perhaps setup a small project and build it.
I found several links that might be useful for you.
And DBlack's question on gis.stackexchange
Which is not as relevant as it could be. But without more info from azteca it looks to me as though they simply use the data via sde. If your data is in postgis/sde (pg_geometry) then at least the gis data side of cityworks should be supported (contact azteca for verification).
I don't see anything on their website about the supported rdbms's (for the asset_db side) but they do state "A key element of Cityworks' design is its flexibility ". I am relatively certain they do support the major rdbms player, mssql, oracle, sybase, informix.
With the google search "cityworks database postgres" I found an interesting link for an individual that would be a good contact for you. You might take a look. I did not feel I should post here.