There is the following statement in the datasheet:
In the absence of a video input signal, the LMH1980 outputs are logic high except for the odd/even field, which is undefined and depends on its previous state, and the composite sync output.
Unfortunately in our application it is not the case.
If the videosignal is switched off the logic state of VSOUT unpredictable.
Sometimes the logic state changes immediately to "low", sometimes it stays "high" and changes to after 30 seconds.
But the signal never stays at a logic high.
We also made test with the LMH1980 Evaluation Board and we saw the same behaviour.