The first thing I would do is attempt to duplicate the problem using a ADV7612-7511 or ADV7842-7511 evaluation board. The 7511 and 7513 are identical except for package and bus width.
Assuming the TV works correctly on the evaluation board then I'd check the custom software driver. It might not be handling the HPD correctly or HDCP. HPD cycling will cause the 7513 transmitter to power down and it has to powered back up again after the HPD rising edge is detected. There are overrides to this power cycling.
Also monitor the 7513 Monitor sense and HPD detect bits.
If the TV is having problems accepting the timing from the source it may lock onto it momentarily then drop and retry.