What does your tab order look like? are there other fields/buttons in your tab order? (Select Set Tab order... from the layouts menu to check.)
Does your drop down list have the arrow option specified?
Thanks for your help. I had the other fields on the layout set for no entry so the client couldn't edit them on this layout. After I removed the restriction and set a tab order the list closes normally. Is there some other way to get it to work and have the other fields set for no entry?
Buttons can also be added to the tab order. You might try adding a small, invisible button that does something innocuous if accidentally clicked and make it be the second item after the drop down list field in your tab order.
An OnObjectSave script trigger that performs a script with Commit Records may also work. I use that trick to make sure data pickers are properly dismissed on some iPhone layouts.