At what point does one database per client become unfeasible?
Managing 100 or 500 databases is really not all that different from managing 5 or 10 - you just have to embrace automation and have a scalability plan in place (and don't plan to use high-cost-per-database features like mirroring across all clients). 

At my previous job we used this architecture and I would never once have ever thought of merging two clients into a single database, even though some of the challenges can be "hard." 

The big benefits are independent recovery models (a can be simple, b can be full, etc.), the ability to restore to a point in time (or remove entirely) a client without disrupting others, the ability to seamlessly move a resource-heavy client to its own storage or to a completely different server with very little in the way of transparency (you update a config file or table that tells the app where to find that client).

I address several of the objections, and/or how to approach the problems, in these posts:


Handling growing number of Tenants in Multi-tenant Database Architecture
Multi-tenant database using SQL Server 2008?
Automation of backups of Large Number of Database


That all said, I don't think any of us can tell you the point at which management becomes impractical for you - just know that whatever specific challenges you come across, you can ask about those problems individually.