Daniel,
You are probably seeing two problems.
1. SPI bus interfaces aren't really designed for such long distances because of the high data rate. It seems like you're seeing data corruption. You might be able to fix this with either a series or parallel terminating resistor. You'd probably have to put a scope on the SCLK and MISO lines to tune the resistor value. But probably you should find a way to shorten the connections.
2. You're also probably seeing a voltage drop which crashes the Lepton when it performs a FFC due to the inductive component of the long power lines. You might be able to fix this with a large-ish electrolytic capacitor connected to the breakout board. Something like 220-470 uF.
Ideally you wouldn't have a long connection between the module and the computer. If you must then you might consider moving over to one of Group Get's UVC USB Camera modules since they can run up to a few meters from the computer, but of course the software would end up being completely different.
Hope this helps.
Regards, Dan