Other than the limits to a party's patience, there are no limits to counter offers. However, the counter offer from the bank may well be their bottom line.
First, try to determine whether the initial asking price was in line with current market values. If so, continue.
How significant a difference is there between the rate your lender offered and that of the bank--and is it still available? Remember too that a stated rate and APR are not the same. Some of those closing costs your lender is charging affect the overall rate. Compare the APR each is offering. Then decide on the lender, based on how long you anticipate living in the house, as suggested in another post.
Then decide whether you want the home enough to accept the bank's counter offer or continue to negotiate. If you decide to negotiate further, you might try negotiating the rate and accepting the other terms if they are acceptable.