I had a similar problem. I dated the shop owner and married her. But then i decide to divorce her after 3 minutes lol.
I went back to her shop, and there was a man running it instead; note: i bought the shop, so she was working for me. So, i believe if you buy the shop, there should be some one to replace the dead shop keeper.
If you already own the shop and no new keeper. Sell the shop, then buy it again when some one has decide to run it. You must also consider the grown of the economy in that area. If the economy is poor no one will be want own and run the store. To counter this problem, ensure you spend money in that area, to make the economy viable again.
Note: easiest and simple solution, go on the the road to rule, and open the steal skill chest, that will enable you to just take it with out with out and shop keeper.
Hope this has been informative
Cheers