For my sins I have a Deau. Well, actually I get quite defensive of the old girl, she does exactly what it says on the tin and does it well.
Check out the owners' forum if you haven't already
http://www.deauvilleuk.org/forum/index.php
They are generally very reliable, just a few quite well known issues, mainly easily sorted.
Fuel pump points often cause issues, you can get Wemoto replacement points for around £20, and there's a mod to fit a diode which cures the points burning issue, excellent article
here . Alternatively you can fit a Facet pump for around £35 with the various fittings.
PAIR valve faults can sometimes cause backfires, simply disable it.
The reg-rec is nowhere near as prone to problems as on the SV650, but it isn't unheard of.
Very rarely the carb diaphragms can fail, but pretty uncommon. Similarly coils are fairly bombproof, can't recall hearing of one failing but it must happen. The 700 version had some faulty plug caps, but those on the 650 seem to go on for ever.
Your issues sound rather like it could be switchgear, again not common but I can remember a few cases. Take apart and thoroughly clean/lube usually sorts it. The main 30A fuse in the starter relay can get corroded, it's behind the right side black panel below the seat, and clean/check all other fuses while about it.
I'd also recommend Iridium plugs, just remember there are 4 of them!
Go to the forum if you're not already on it.