Is the computer that needs "print" hit twice the computer that is hosting the shared printer?
Or just another computer among those computers that do not need to have print hit twice?
If the latter, compare the problem computer's print settings/configuration with another computer that does respond/print as expected.
And look in Reliability History and Event Viewer: either one or both may be capturing some error, warning, or informational event when the first attempt to print is made.
Do so for both the printer's host computer (if different) and the computer that needs to be hit twice.