Yes a bank can ask for a higher down payment. This has happened to a couple of my clients. When the bank did a final check the peoples income to debt ratio was just a little bit high and to off set this the bank had the buyers put up between $200 and $500 more for a down payment to get this back in line. These banks right now are under a lot of scrutiny and little things like this have to be done to make sure the loans meet all the guide lines. I hope this is helpful to you.
until you clear underwriting,expect anything these days. With rates so low underwriting could easily last right up to closing day. Most banks give new sales priority over refinance, but the wheels turn a little slower now.
In this current lending climate I'm telling my clients to get ready for anything and hang on for a bumpy ride. If your lender pulled a credit report or you had a life changing event (job change, divorce, etc.) then it's possible the lender would want more money for your down payment. I had a lender ask a client for college transcripts! Crazy stuff happening these days.