Until I tried to checkout, modify and commit with SVN itself:
svn: Commit failed (details follow): svn: MERGE request failed on '/' svn: Can't open directory '/home/ivan/bsite/svn-repo/db/transactions/0-1.txn/transactions': No such file or directory
No matter what I tried SVN can’t commit into a repository without an error.
Turns out this problem is caused by Apache and Subversion being compiled against different versions of the APR libraries. I got it fixed by rebuilding apache and subversion from their fresh sources.