As CJ says, try without the splitter. but it may be the many things.
I had something similar previously:
I used to run my Freesat box from the utillity room via HDMI extenderd (dual Cat 6 twisted pair cables) to living room.
Every time I turned on or off the lights in the *hallway*, I lost signal for 1-2 seconds on the Freesat box.
I quickly came to the conclusion that the electric surge from turning power on or off (or may even just the change in magnetic field) generated a wide-band interference in the Cat 6 cable. This caused the drop-out in signal. The electrical witing was running inside the wall, but still interfered with the Cat 6 running outside the wall. See pics below.
I have since relocated the box to the living room, and do not have the problem anymore - the antenna coax ironically runs on a similar path between almost the same two endpoints as the Cat 6, but is probably situated slightly furrther from electrical wiring. However, I believe the key factor in difference is that the Coax is shielded, and the Sat signal may be higher up in frequencies, or something similar. It is less prone to interference.
Back to your situation:
Check that there is not HDMI cable running very close to electrical wiring (on which a spike may be induced when your microwave turns on).
Note these may be in the wall, so try moving HDMI cables away from wall.
Check that the HDMI splitter is not situated very close to electrical wiring.
The electrical wiring need not be the actual power lines going to the microwave, it sufficies they are on the same circuit.
If you can, try some better shielded HDMI cables. This may help, but HDMI tends to be a opaque market ("gold cables" and the like).
Finally, check if the Sky box is on the same wiring as the microwave (and poss the light switch).