Is there any place in the Rulebook where it says that when a unit has a Supressed marker if this unit gets another then becomes eliminated.
No. If a suppressed unit achieves another suppression result - nothing happens. It just remains suppressed:
Each unit in play may have a maximum of one of each of the following markers stacked upon it:
WEAPON (any... )
The phrase one of each of the following means that a unit can have:
1 Suppressed marker and
1 Veteran marker and
assigned to it at the same time. But it may not have 2 of the same type of marker assigned to it. For example, you can't add a second veteran marker to a unit that already has a veteran marker. You can't add a second suppressed marker to a unit that already has a suppressed marker.