As long as you maintain each printer and keep a proper calibration, go for it, this is what they were designed to do, I've even made replacement parts for myself.
Unfortunately the RepRap project just shut down on 1/15/16 due to their lack of sales.
I have a reprap that came from a reprap, and has made another reprap.
Just make sure that when printing out the pieces for the next you are properly calibrated, otherwise the next machine might be built crooked;
Your only limitations will be the electronics pieces and the small amount of hardware that you will need to buy.
There is a 3D desktop printer RepRap which can print most of its own components.
Assuming each printed printer will print the next one and so on. Are there any limitation how many times this can be achieved?
For example somebody printed for me printer and I do the same for my friends and they do the same for theirs. Can this go forever (since 3D model stays the same), or there are any serious side-effects/disadvantages of doing that continuously?