Yes, recycled PLA loses mechanical properties.
According to Dr. D-Flo's excellent video on Recycling 3D Prints and Waste plastic into Filament (PET & PLA) it loses mechanical strength during every thermal cycle - i.e. when it is printed, when it is melted down for recycling, when it is next printed, etc.
Manufacturers account for this by mixing in "virgin" PLA. So "recycled PLA" is really a mix of recycled and new PLA. This will lessen the extent to which the recycled portion will affect overall strength of the result.
I do not know if/how manufacturers would account for how many thermal cycles the PLA you supply has been through.
If the mix of virgin/recycled PLA has more virgin than recycled, then it may not matter. If the mix favoured recycled then each batch would be worse than the one before. I suppose manufacturers can test a sample from the beginning of their re-extrusion, and if they find it too brittle (etc.) they can change the mix before continuing.