Actually, I don't know how it's possible to get such an issue. Possible (but unlikely) reasons are:
1. Server-side caching (using System-Cache plugin, native caching in webserver, caching proxy, etc.)
2. You setup another page for mobile homepage, that's why changing of desktop homepage doesn't affect mobile one (but it affects homepage only).
3. You setup mobile domain for your website, and move your website to another server. As a result, mobile and desktop domains could be resolved to different IP (one of them corresponds to old server).