Something is dropping the system voltage so low that it can't hold the main relay or the starter relay closed. This can either be a massive current draw (short circuit), massive resistance, or a battery problem.
What makes you say the battery's OK? They can be breaking up inside and shorting etc and do all sorts of strange things. Is it new? What's its history? An intermittent thing like this is hard to test for, but what tests have you done?
Massive resistances can be things like battery terminals coming loose, the main chassis earth being lose or in poor condition, or poor connections elsewhere. Given that everything's dying it's likely to be somewhere "upstream". In the past I've had problems with starter relays - they have solid internal current paths and this eventually rot, causing similar symptoms to yours.
There appears to be a wiring diagram here.
If it's a short circuit then it should be blowing a fuse unless it's in the first non-fused part of the circuit between the battery and the starter relay (top right) that has an integral 30A fuse. So if it's not blowing fuses then first check that they are all actual fuses and not bits of tin foil / wire / nails courtesy of some bodge artist. Then if they all check OK, check the wiring between the battery, starter relay etc.
The final possibility is that the battery is goosed, such that once you're underway the only thing keeping the bike running is the alternator. If there was a short circuit between the reg/rec and the battery this could then cause a similar problem, so although it's unlikely, it's worth checking all that wiring too.
Does it always cut out after a mile or does it vary? Is it always on the same corner / manoeuvre, or pretty random?
My favourite place to start looking would be the starter relay. Be careful - if it IS rotten then it'll pretty much fall apart. M&P do pattern replacements for a lot of bikes, and if they don't do one for yours you can probably make one of them fit OK.
Give me a yell if you need any more help 
arrrf.
