Had a few of these on our 200 surfaces in the organisation so I think it may be a bug...different Docks different Surface Pros.
Surface Pro i5 (Latest updates for 1709, latest drivers for 1709 etc...). Kept in a drawer overnight. Battery goes flat. Plug into the surface dock 2 (latest firmware) and get a white flashing light on the charging connector. Check connector, re-seat etc..same problem 100%. Connect to the normal surface charger, solid white light, wait 5 mins, gets a bit of charge and then plug into the Dock - have a solid white light and the Surface happily charges.
Seems like some sort of bug to me...and a bit of Googling seems to show lots of others having a similar problem. Not a big issue for me but those in the organisation who are not confident with technology log a support call, have lost their charger, can't work, asks for their trusty (rubbish) desktop to be returned, rants...etc..
I have obviously run through all the various Microsoft Troubleshooting guides but nothing quite fits with my circumstances.
If anyone has experienced this exact scenario and has an absolute solution then I am all ears (even if that answer is it is fixed 1803).