Mike,
I don't know who your vendor is, but I certainly can tell from what you have mentioned above that either he has no idea about what he is talking or he is hiding information from you. What is meant by "long time". What kind of damage can happen to compressor?
The one problem that I can foresee is that if gas is recycled through anti-surge valve or for that matter through any recycle mechanism, the temperature of the recycle gas will be higher than the fresh feed to compressor inlet. This is quite solvable. Just by having a properly designed air cooled heat exchanger in the recycle line you can avoid this problem.
However, one important point to be noted when specifying a compressor, specifically in process gas service, is to provide the compressor vendor the entire flow range including maximum turn-down and the maximum variation in gas composition, gas molecular weight, gas density etc. This is generally done by defining various cases or scenarios as permutation /combination of flow rate, gas composition / properties or in a nutshell the entire performance envelope of the compressor
Most performance problems related to changed operating conditions with compressors arise because due diligence was not done in defining the entire performance envelope of the compressor during the engineering design stage.
Regards,
Ankur