There is a long history documented on various forums of wandering zeros on Pulsar and other more budget friendly thermals.
Supposedly it’s specific to certain models and newer Pulsars don’t have the problem but I’m skeptical and apparently so are you.
There are advantages to the higher shelf thermals and none of them have a meaningful number of complaints about not holding zero, but…
I’ve found that no dollar amount thrown at thermal scopes guarantees a trouble free experience.
The Trijicon thermals are currently the most reliable scopes on the market. Unfortunately they have outdated features. N-Vision thermals have better features with some degree of sacrifice in reliability.
Under 10K, the Nox35 is my favorite thermal by far for daily (nightly) use, but if I had to trust my life to it I’d buy a Trijicon Reap-ir (any generation) for sure.
If N-Vision can improve consistency in QC and standardize their (normally excellent) CS, they will put Trijicon and others out of business.