The former Soviet republic near Afghanistan has lurched through a series of political crises since Askar Akayev, the former president, fled violent protests in March 2005.
Parliament voted 38 to 25 against reinstating Kulov, little changed from the 39 to 23 vote rejecting him a week ago.
Due to confusion over the country's constitution - a new charter weakening Bakiyev was adopted last month and then another one handing back most of his powers - it is not clear how long the deadlock might last.
The constitution appears to allow Bakiyev to dissolve parliament if his candidate for prime minister is rejected three times.
But lawyers working for parliament, Bakiyev's office and an opposition leader have all said that under interim rules Bakiyev can nominate Kulov as many times as he likes.