PMO: A Mgmt whim?

In many organizations, PMOs are started as a brainchild of a new CxO, many a time to keep up with the neighbors.
There is an initial honeymoon period where “initiatives” are started with fanfare.
Then things die down..
Enter a new CxO. His question – what the hell does this dept do anyway??
Next cost cutting round – exit the PMO dept.

How can we prevent this PMO lifecycle executing the same way everywhere?

Here I am referring mainly to SMEs.

Cheers…