\documentclass[10pt,reqno]{amsart}
\usepackage{amsmath,amssymb,amsthm}
\usepackage{catchfilebetweentags}


\section{Test with my patch counts to say 11}
\label{sec:test-with-my}


But if I close the file  after 10 and reopen it it incorrectly inserts the tag 10 not 11
%<*test-catch:1>
1
%</test-catch:1>
%<*test-catch:2>
2
%</test-catch:2>
%<*test-catch:3>
3
%</test-catch:3>

%<*test-catch:4>
4
%</test-catch:4>

%<*test-catch:5>
5
%</test-catch:5>


%<*test-catch:6>
6
%</test-catch:6>

%<*test-catch:7>
7
%</test-catch:7>
%<*test-catch:8>
8
%</test-catch:8>


%<*test-catch:9>
9
%</test-catch:9>


%<*test-catch:10>
10
%</test-catch:10>


\section{Test without my patch till 10}
\label{sec:test-without-my}

%<*1>
1
%</1>

%<*2>
2
%</2>
%<*3>
3
%</3>

%<*4>
4
%</4>


%<*5>
5
%</5>
%<*6>
6
%</6>


%<*7>
7
%</7>


%<*8>
8

%</8>


%<*9>
9
%</9>


%<*10>
10
%</10>


%<*11>
11
%</11>
\end{document}