D.Va has access to two items that grant her semi-permanent Shields until her Mech is destroyed.
Solo Spec
+25 Health
When you mitigate damage with [Defense Matrix], gain Shields equal to 10% of the damage mitigated, up to 100. Resets when your [Mech] is destroyed.
Chip-Damage Diverter
+50 Health
When you deal damage to Barriers while in your [Mech], gain Shields equal to 10% of the damage dealt, up to 200. Resets when your [Mech] is destroyed.
Both of these grant Shields and consequently remove the Shields when the Mech is destroyed by an enemy. Upon using [Self-Destruct] and [Call Mech], the up-to 100 Shields granted by Solo Spec remain, those of Chip Damage Diverter are removed and have to be reobtained.
I am unsure which one of these is the bugged one, but given the flavour text of the removal condition for the Shields being identical, they are either supposed to both lose their accumulated Shields using Self-Destruct or both should be retained that way.