I get pretty much the same issue, except when I curl the mouse to turn it back on, the display disconnects within about a minute.
Wish I had known about the issue. Don't think I would have picked it up today. Bummer!
Anywho... Submitted a bad review citing the issue both on the MS Store and BestBuy (where I bought it). I suggest more do the same. Squeaky wheel gets the grease and all.