I agree its probably a hetrodyne cause by intermod from the active repeater and at least one other transmitter nearby creating ghost signals on your repeater input.
Several tests you can do without test equipment is go to the repeater site and disable the transmitter while listening to the local speaker on the repeater. If the interference goes away with the repeater transmitter going off then your repeater is part of the intermod problem. If the interference stays then two or more other transmitters are probably causing the problem. See if your repeater has an isolator or circulator on its transmitter before the duplexer or band pass filter. If not then your repeater is a prime candidate for causing its own interference.
Another test can be run using an SDR dongle receiver as a spectrum analyzer and monitor the entire VHF and UHF bands looking for a signal that pops up and coincides with your interference. You may be able to pick up the weak interference on the repeater input frequency but what your really looking for is another system that might be contributing to the interference on a completely different frequency. It can even be on a different band as I found helping track down some interference to a Coast Guard repeater which was on VHF and part of the interference was caused by a UHF amateur repeater nearby.
I also like to tap into the receive cable from the repeater duplexer and monitor with a spectrum analyzer to get a better look at the problem and compare interference levels to normal user levels, etc.