Could severe solar activity play cause problems for Pilotless Aeroplanes?

No. They've had autopilots that can fly planes by themselves for over 10 or 15 years now. Maybe not as sophisticated but so far they haven't had any problems with solar storms. Lightning in lightning storms is something much more to avoid.

Mind you, during major solar storms, planes are banned from flying over the polar regions, and I'd presume that pilotless planes would also be baned from the polar regions.

Severe, yes

Normal, no

A severe solar storm can knock out transformers, satellites and radio.

However, technology like this is shielded from charged particles which interfere with electrical equipment, so I assume rthis plane is also shielded.

However, if the flare was large enough, presumably communication with the pilotless plane could be lost or if severe enough, the plane could be knocked offline.

The chances of this scenario are astronomically low though.

A solar storm would have to fack the van allen belt up pretty bad for that to happen.