My question is, do I have any ground to stand on by holding firm that the seller (or bank I guess in this case) pay half of the closing costs, or is it likely that if I don't agree to pay the full cost, the bank will reject the sale and then either go to the next highest offer or foreclose on the house?

That company ended up rejecting my policy and I had to find another company.

Most of them made a hasty decision to reject the app, based merely on ONE negative review of it: that of the original poster. 

If they reject your offer, so what...on to the next.Can I ask what your strategy is?

What happens when the city rejects the design because the siding is not properly fire rated (this is just one example).

He then finds out the person who will be helping him manage was a tenant applicant he rejected a couple months ago.

You would have to look local specific laws regarding what you can reject for.

I have been searching for properties on the MLS and talking to realtors and getting our offers rejected more than several times on several properties, I'm guessing due to competition of other people being in better position than us.

If the former, the Broker, or his agent, have only a duty to present your offer to the seller, not to call you within any time frame (although it would be courtyess and probably good business) until such time as the seller either accepts, rejects, or counters your offer.  

The seller can reject them all if they want... even an offer over the listing price!