Voltage drop pulse transformer
You cannot simply pass DC through a transformer without repercussions. The primary winding is basically an inductor and any DC level is dragged to ground so, the DC level coming out of your driver is facing a big hurdle but coping enough. However, the voltage it is now producing is seriously reduced and, if the pulse transformer had a lower primary DC resistance it would be even more compromised. 

The only option you have is to AC couple the driver to the pulse transformer primary but this then exposes a problem on the secondary; if the pulse width is 50% then the output will be equally positive and negative but the positive peak will be 50% of the former amplitude without the pulse transformer. If the duty cycle is a lot lower than 50% then the positive peaks will be closer to the former amplitude but, if the duty is high the positive peaks will be not enough to activate the mosfet.

This means you have to do two things: -


AC couple the primary as previously explained
Restore the DC on the secondary using diodes like this: -




D1 and C2 act to keep the voltage at D1's cathode not less than about 1 volt negative and the other components provide an active clamp to discharge the MOSFET's gate capacitance when the output does fall below 0 volts.

It's never clear-cut with an isolated MOSFET driver.