Corrupt Time Machine
This sounds like it could be a failing hardware component.  

Swap any connectors, try with a different cable, etc. IF this is a some major brand usb 3.0 external drives have internal usb 3.0 connectors fail frequently. Try it with a usb 2.0 micro cable and it may work fine at a slower speed.  If an external drive, you may be able to put into a drive dock to avoid issues with the factory housing and connectors.  

As soon as you get a stable connection, use the dd command, or something like daemon tools or 7 zip or whatever compression tool you prefer to dump the contents of each partition you don't want to lose to an iso to attempt recovery from later.  This is assuming you have another drive with sufficient capacity.  Let this complete before doing anything else so if the drive itself fails you have something to fall back to.

If you don't have any backup media, a clonezilla live cd could let you see the partition table really looks like and whether a filesystem to attempt to repair is still detected.

Consider the exFAT format for drives that need to walk in both worlds, and use a single hardware drive for TimeMachine if possible.  It has not worked well with multi partitioned drives in my experience, although it is a fantastic backup solution. 

Hope this helps!