Washing PCB for picoamp circuitry
My guess would be the solder flux.  Rosin based fluxes are great and I've never had any problems.  The water soluble, no-clean and other fluxes have given me no end of headache.
You might ask whoever is making your boards about the flux, maybe you can try a different one.

As far as cleaning, I've only had mixed results.  Once the flux gets in there it can get under surface mount components and it's hard to get out.  And what to clean with?  That would depend on what the flux is.  For a water based flux try hot soapy water, there are lots of stories about putting PCB's in a dishwasher for cleaning, but I've never tried this.  If it's a "no clean" flux then I'd contact the manufacturer and see if they have a recommendation on what could be used to clean it.