You can try installing the Add-in in steps as follows:
1. Open the commad window (Start>Run type cmd and press enter)
2. Navigate to the path where the installer (SharePointRS.msi) is stored
3. Execute SharePointRS.msi SKIPCA=1 This will do a files only installation of Reporting Services Plug-In
4. CD to %temp%
5. Execute rsCustomAction.exe /i to auto-configure the installed  files.

For detail, please see http://msdn.microsoft.com/en-us/library/bb839479(SQL.90).aspx .

And you can find installation log in %temp% folder, the file name is like RS_SP_xxx.log.

If the SSRS mode is reverting back from Integrated, then you probably do not have a good configuration  in SSRS. When this occurs, I generally start over with the process. Make sure you are not using Local System or Network Service for the service accounts for SSRS. Then, create a web site that you will use for SSRS in IIS.

Next, go to SSRS configuration manager and start at the first step and progress through the steps. The key step is creation of the database. You can skip the Report Manager step since report manager is not used in integrated mode.

Perhaps GuYuming's advice will be all you need, but it sounds to me that the config manager may be the issue and not the add-in.

Either way, I hope you are able to get it up and running.