I can see the problem, getting PHP timeout errors when trying to edit the template.
I've done quite a bit of debugging on it myself, but I need the developers to take a closer look, so I've escalated this to them and I'll report back when I have something from them.
I mentioned that I have another ticket with very similar symptoms, and on that site I found that if I downgraded Blocks to 1.2.2 I was able to edit the templates again. I didn't try on your site, but it may be an option for you temporarily.
The developers produced a temporary patch to fix the problem with the current version of the plugin, but its not a permanent fix, they still need to work on that.
We will soon be releasing an update for Blocks, but its not clear if the permanent fix will be ready in time for it, and if not a different patch would need to be prepared and applied.
If you've already reverted to the previous version of Blocks as discussed above, I suggest we wait for the plugin update—which may include a permanent fix—and if not then you can update and apply a new patch until the permanent fix is included.
Just a quick note to say that the update containing the fix is now available to all users, so feel free to update, you won't need to re-apply the patch.