It is most likely connectors in your HIDs. Dosen't seem like your HIDs need replacement since your low beams work fine. I am no expert on this at all but it seems to me that your wires have water damage, faulty, fried, or not connected properly.
Let us know, I am curious as well!
2007 E90 328i - Titanium Metallic l 19" VMR V710 l H&R Trak+ Spacers l Mtech Rear Lip Spoiler l Hamann Front Lip l Eibach Sportline l AA N52 Signature Exhaust l OEM Blacklines l MTEC V3 AE l 6000K HID l Nokya 7000K Fogs l MTEC License Plate LED l Interior LED l 15% Tint l BlackVue DR380G-HD + PMP