I don't understand where an axle nut has anything to do with crank arms, since you're talking about a "nut" vs. a "bolt."

I'll assume you mean the nut that secures the crank arm to the bolt that protrudes from a square taper BB spindle.

1-pull the crank arms (both sides).
2-inspect the threads on both sides for any damage.
3-inspect the nuts from both sides for damage.
4-swap sides with the nuts, tighten, see what happens.
,,,a) If the other side is now loose, it's the nut.
,,,b) If the same side keeps getting loose, it's the bolt.

5-If it's the nut, replace. I've found them a Lowe's before. I wouldn't recommend a lock washer, but you can try it.
6-If it's the bolt, you can chase the threads, or you can switch to a different bb.