Hey, sorry bout your razor!
But I've had the same problem, ordered a 2nd hand razor online, polished it up till it looks good again.
While polishing I left it wet on the table and went for dinner (1 hour) when I came back the blade was ALREADY rusting.
This happens is the surface is fat-free. Just use some good oil on a tissue and rub it on there..
When it's wet, you can see the water running away from the blade! But ofcourse, always put away dry also...
Edit:
By the way, stropping paste is fat too, do you use paste on your strop?