Traditionally, online credit card processors are used to process
payments for online stores, etc. These processors typically charge a
monthly fee (~$25-50) and a percentage of the amount (.5 to 1.5%) per
transaction.

My question is that I am looking for a credit card processing company
that will charge solely a fixed monthly fee for a non profit
corporation. Or even for free!

We do not mind paying the monthly fee, but (.5% to 1.5%) on tens of
thousands or perhaps hundreds of thousands of dollars each month will
amount to a huge amount of fees.

If this helps, it also helps the credit card company because their
services could be tax deductible.

Thanks

In General, the card associations (V/MC) have a set of
discount/transaction fees called InterChange.  InterChange is better
understood as Inter-Member-Bank-Exchange.  The Members of each
association (V/MC) are either Issuers (issue the cards) or Acquirers
(Acquire the merchant transaction) or Both.  Interchange actually is
paid from the acquirer to the issuer - based on the transaction -
through the clearing systems (V = BASE I & II and MC = INET & INES). 
This is the primary component of the basis charges to a merchant. 
Atop this, each association has Dues & Assessments (.0925% V & .095%
MC) which is the funding of the associations themselves.  Then you add
the network (authorization and settlement) charges, the sales
organizations charges - and out the other end comes your discount rate
and transaction fee.  Because these are mostly FIXXED costs - you will
NOT find any 'free' services or flat rate services.  Sorry to bring
the bad news.