Turns out that the post (or rather the whole table) was locked by the very same connection that I tried to update the post with.
I had a opened record set of the post that was created by:
Set RecSet = Conn.Execute()
This type of recordset is supposed to be read-only and when I was using MS Access as database it did not lock anything. But apparently this type of record set did lock something on MS SQL Server 2012 because when I added these lines of code before executing the UPDATE SQL statement...
RecSet.Close
Set RecSet = Nothing
...everything worked just fine.
So bottom line is to be careful with opened record sets - even if they are read-only they could lock your table from updates.