@brianjastram, I think my colleagues in Washington DC have experienced a similar problem to yours, and after a bunch of troubleshooting, we figured out that it was due to electromagnetic interference in the analog signal line from the tipping bucket to the counting device. They had used unshielded cable and also had some unshielded connectors on the outside of the box. We solved the problem only after shielding the entire length of cable, and grounding one end (and only one end) to the battery negative.
I had never seen that my other installations, and those same stations worked fine our Ann Arbor office but started showing those tips at odd times of day in busy urban Environment at our DC office. Our clue was that two tipping buckets sitting next to each other on a desk were showing those random tips at the same time.
Let us know if this might make sense for your situation.