I used to have this issue and I've posted here about it without a resolution and the problem is exactly as you described. Here is what I can tell you. I had this happen on two repeaters and here is what I had in common.
1. Both running DSP (I was using software to generate PL)
2. Older versions of software.
I have since upgraded software to latest version and I no longer use DSP and use the repeaters internal PL. I never bothered trying to figure out the problem any further. Mostly because I have interest less focused on deployment of analog systems and doing the above steps gives me good audio.