The 32-spoke wheel might be a little weak for 300 pounds, but there are some things you can do-

1) Get the rear wheel tensioned, stress-relieved and trued. A good wheelbuilder can do this for some $50. Factory wheels often have uneven tension and may not be stress-relieved at all, and that will cause the spokes to fail earlier than they should.
2) Ride "light"-- don't jump curbs, take the weight off the saddle when going over bumps, etc. This will keep the max stress lower on the wheel- it's repetitions of max stress that cause wheel failure.
3) When the wheel starts breaking spokes (after your third broken spoke) (which if you do 1 and 2 may be never), trash it and get a 40-48 spoke hand-built wheel with DT Alpine spokes and an eyeletted rim built on a good Shimano freehub. That's what the tandem folks do. Mountain bike right?- so maybe a 36-spoke wheel would be OK if not used really harshly.