Will PAEK polymers hydrolyze in concentrated sulfuric acid?
I resist concluding this but nothing else I can think of makes sense. The only way the polymer solution to become less viscous is through a cleavage of bonds reducing the MW of the polymer or dilution. Cleavage at the ether linkages would require reduction in an oxidizing environment or nucleophilic aromatic substitution which this polymer lacks the electron-withdrawing groups to effect, so those mechanisms should be eliminated (I concur with your colleague). Thus we can deduce that the cleavage must be occurring at the carbonyl groups.

To cleave the polymer at the carbonyl groups, the PAEK is likely undergoing an electrophilic aromatic substitution at the carbonyl groups. Though not commonly utilized, it is possible to substitute any electrophile on an aromatic ring in including acyl groups (especially with sulfuric acid which provides a high concentration of $\ce{H+}$ electrophiles) as shown in Figure 1 — essentially Friedel–Crafts acylation in reverse.


Figure 1. Electrophilic Aromatic Substitution Removing an Acyl Group.