That is absolutely not true. You literally just made that ***up, or are playing with clueless Dragoons who aren't paying any attention to their pet.
The wyvern has like 40% DT, Spirit Link fills its HP and adds a regen effect, and Steady Wing is ridiculously strong with proper swaps. The wyvern is near unkillable at this point. The DRG dying and then not having the CD up is more an issue.
Odin from the Wave 3 boss is the only thing that kills them, and even then we have the CD up, and with so many COR generally another one if needed (just via normal random deals not any targeted to give the wyvern back).