refinance mortgage rate

This seems like a shockingly simple statement but more often than not, many of us do not even do that. Think about how ladies would spend a lot of time browsing shopping items such as clothes. Comparing prices, designs and quality among others.

The same detail and care should be applied to mortgage rates. Even more so since a mortgage could potentially last you a long time or cost you an arm and a leg. Or it could exceed your monthly cash flow should the bank choose to raise your rate. Be careful as they would simply raise it without warning. That is when you find out much they actually care about you.
xBL.-Same bank.

It is likely that your existing bank would want keep your mortgage. You might get the odd bank which would not care if you stayed or left though. Show your current bank the best offers from the other banks. Since their whole livelihood depends on analyzing their competition, they would be extremely aware of the offers even before you even show them.
xBL.-Another bank.

If, however, they do not even attempt to keep you on, it is nothing for you to worry about. Simply choose the bank which you have already researched on which has the next best offer. Find out what are the transfer fees though so you don't get a rude shock.

The reason why your current bank seems disinterested in retaining you could simply because your business is not his main priority now. This does happen and there are definitely other banks who are interested in your segment and who are more than happy to take your mortgage. Squeeze the best rate out of them as much as you can. This would be the best time to do so, before you sign on the dotted line.