As long as there's not an associated paper ticket (which should be very rare these days), losing a boarding pass is not an issue.

Back in the old days, either the agent would take the paper ticket in exchange for a boarding pass, or staple it to the BP and you'd turn both in at the gate. In either case, don't lose it.

Amtrak still uses paper tickets for most of its routes, and there have been a few people bitten by this -- they lose their ticket, and assume it can just be reprinted like a boarding pass. Nope.