patch prompt

Just guessing, but I think it is a permissions problem.
At least it sounds to me like that.
You for sure run IntelliJ as user and maybe the patching can only be done as Administrator which doesn't work and thus the patch is not applied correctly.
If this is the case, either download 10.5.1 manually from the website and install, or run IntelliJ as Administrator (right-click->Run as Administrator) and do the patch then.
If I was right you should maybe report this as Usage Bug.

one more option is to relocate idea system folder to a permited path. Copy %HOME_DIR%/.IntelliJIdea10 to a new place, then edit bin\idea.properties (change paths to required):

# path to IDEA config folder. Make sure you're using forward slashes
idea.config.path=D:/dev/tools/.IntelliJIdea10/config

# path to IDEA system folder. Make sure you're using forward slashes
idea.system.path=D:/dev/tools/.IntelliJIdea10/system

# path to user installed plugins folder. Make sure you're using forward slashes
idea.plugins.path=D:/dev/tools/.IntelliJIdea10/config/plugins

Don't sure (normally this shouldn't happen), but  you could be prompted to reindex and enter license number.

regards, Alex

Thanks for the help everyone. Run as administrator worked.

How should this help?
The HOME_DIR is user-writable so the system directory there cannot be the problem.
What is not writable by normal user under UAE is the IDEA_INSTALL_DIR if it is located in "C:\Program Files".
Because of that the patch can be downloaded fine to the system dir (at least I think that is where it is downloaded to) but then not be installed to the protected directory without administrative rights.