Analog sampling over long lines freezes ARM chip

Wawa:
Between six wires and a common ground?

No, between any wire and any other wire.

Wawa:
Do you use internal pull up or external resistors. What value?

Since I have to determine which two wires are in contact, each Arduino analog input has a voltage divider of total 1 MOhm <== EDIT: this is mistake, sorry, the total divider resistance is about 15 k Ohm

Wawa:
What sort of wire. Shielded, twisted?

Two simple 3-conductor signal cables. No shielding, to twisting or braiding.

Grumpy_Mike:
You are not going to affect anything in regard to your sample rate, they are way too slow.

Unfortunately I need to catch some very brief contacts, of the order of 10 microseconds