I have now tried more times to get the shop running. But every time I adjust the prices, the shop no longer works as it would not be there

if it's not showing up it means your not matching the names correctly or your not following the Title case naming convention 

uMod - "There is something wrong with this shop. Please contact an admin" - GUI Shop - Community

Is there any reason that simply removing items seems to mess with the shop?

If you remove the items from the lower half (Shops don't matter) the plugin will think they are missing and auto re-add them at the bottom. It's part of its auto-updater functions.