I doubt very much sag is actually the issue, it would have be SEVERELY sagging to the point of warping the PCB to bring about any real issues. Furthermore how did you come to the conclusion sag was causing your issues? Just merely looking at a card sagging isn't a proper way to diagnose anything really. Did you try propping the card up and rerun your games/test and see if the issue stopped? 
 
PC crashing and resetting during games is 99% of the time a sign your PSU can't cope with the load you're asking of it and tripping its OCP (over current protection) in an attempt to save itself. However seeing as you provided no actual hardware specs like CPU, motherboard, RAM, make and model of your power supply, I really have no idea or suggestions. 
 
PS: Also no, the PCIe slot is only capable of providing about 66w of useable current to your card. Of which that isn't constant either and can and will vary based on load and TDP requirements in an ever changing state (still capped to about 66w)  

TenshiMarcelo
The crashes were solved by an anti-sag holder.

My main question is if bad contact with the pcie slot could have any long term side effects, as in any damage to the card.

As of right now it seems to be operating normally.

If you are operating normally now I would think you are fine and would not expect to have long term effects from the crashed you had , they were just crashes and crashes are a method of self protection