The number of small and midsize companies taking bids for a new banking relationship doubled in the first half of 2010, according to financial services firm Greenwich Associates.

The firm said 20% of midsize businesses, those with annual  revenue of between $10 million and $500 million, have requested competitive proposals for a new bank in the past six months. The firm said 15% of small businesses have done the same.

That’s roughly double the rate in the last half of 2009, and up sharply from a year ago, when just 4% of small and midsize businesses were looking for a new bank.

And in a surprise, they aren’t looking because they’re turning cartwheels about their current banking arrangements. The top reason cited by companies looking for a new bank is that they want to cut the fees they pay, Greenwich Associates found in a survey of 594 companies conducted in June and July.

“Unfortunately, it seems that this high level of activity is being driven as much by negative factors associated with the recession and credit crunch as by positive developments such as an increased demand for capital in step with an economic recovery,” Greenwich said.

The firm said the second-most-popular reason for seeking a new bank was an increase in demand for capital. But just over a quarter of small businesses reported needing more capital in the latest survey period, compared with half in late 2009.

“At the start of this year it seemed clear that a good portion of switching activity was being driven by the positive trend of companies looking for new sources of capital to fund their businesses in the face of an economic recovery,” the Greenwich study said. “Although the share of companies looking to switch banks has increased dramatically since then, this activity does not seem to reflect new strength, but rather, increased frustration with current providers.”

That squares with the findings of the National Federation of Independent Businesses, which says just 6% of business owners in its most recent survey chose financing as their most pressing problem. That number rose as high as 37% in the recession of the early 1980s, the NFIB said.

Though business people may not be leaping with joy over their bank, they have much bigger problems in a slow-growing economy where consumers are still trying to cut back.

“What businesses need are customers, giving them a reason to hire and make capital expenditures and borrow to support those activities,” the group said last month in its Small Business Economic Trends report.