Not sure if the necessary postgres client dll's are on the install media - I don't get to see DVD's any more these days, but what is strange is that these are not automatically deployed as part of the install process. At 10.1 you DO have to manually copy the dll's to your bin directory - surely this could be an install option (ask user which db they are using, and deploy the relevant dll's)?
Anyway, the workaround is to find the dll's listed below. If you are registered properly with the ESRI customer care portal you can apparently get them there, we got them from our international distributor....
Windows 32-bit PostgreSQL 9.0.5 Client Libraries:
Libpq.dll
Libeay32.dll
Libintl-8.dll
Ssleay32.dll
Place these files in the bin folders of your Windows 32-bit Esri client application.
I will no doubt post some further examples of our adventures in PostGIS/ArcGIS integration, but for now am happy to report that with the above fix we are able to use our PostGIS tables.........