The text of the card reads: "during a fight, for each (hit) that causes you to suffer damage, you may spend 1 Cap. If you do not, discard this card"

So is this essentially saying you have to pay for the hits in order to keep the weapon?

Eg. If I get three hits, and I only have two Caps, I still get hit and lose the weapon? Or is paying the caps meant to absorb the hits?

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I still get hit and lose the weapon?

Yes. You always take the hits and optionally choose whether to pay to keep the weapon. Of course, equipped armor can absorb hits to reduce this.

Yeah. Basically laser rifles are finnicky and break easy if you aren't paying to constantly keep them maintained.