There are two 'paths' through an amplifier, one is a 'by-pass' around the amplifier when it's off, the other is through the amplifier when it's on. These two paths are typically controled by a relay switching between them. That relay is a very common place for changes in SWR to be caused. The usual 'cure' is to clean the contacts of that relay, or just replace the thing.
You do want to check to see that the by-pass line isn't 'boogered up' in some way. From there it can get complicated.
- 'Doc
To clarify, the high SWR is at the radio side, not the antenna side.