My thoughts are its scope hookup has issues and is adding in extraneous noise that
the DSO is trying to sync on. Since the signal is both amplitude and phase I'd suspect
outside sources getting into the hookup.
I see this all of the time when people new to scopes do not understand how to ground or otherwise
hook up a scope so they do not introduce spurious signals. That 8 inch lead from the scope
probe is also an antenna. Around here I can see 20-50mV of RF from a broadcast station
maybe 4 miles away with that led connected to the tip.
LIkely the 5351 signal is stable. Though its possible that the MPU is updating it with a range
of possible signals out so you can be seeing the frequency actually chance. If the code is as
supplied likely not the case.
So if I had to guess and the images sent help not, Id say your seeing a broadcast station
getting until the scope via the probe.