This is extremely difficult to diagnose without version or error information, but I can offer a few suggestions.
First of all, it is not recommended to put System.Web.Extensions in the bin folder. If the latest framework is installed, the ajax assemblies are included in the GAC and everything is configured to work properly. By dumping a dll in the bin folder, you are experimenting with version, dependency and trust issues which may cause your application to run slower, different or not at all.
Verify your .net framework installations to ensure the most recent version or service packs are installed on both the server and your development machine. Then double check which versions are actually being referenced by your web project and web.config. There has always been a version problem with ajax between development and deployment (expecially during beta cycles) but as far as why the IIS worker process deletes files in this scenario, you have me stumped.