(Not an answer) I cannot confirm any disappearing acts of sections or subsections using cuted.sty 2012/10/04 v1.5 Mixing onecolumn and twocolumn modes.
UPDATE I can now confirm that the issue can be reproduced using the last update of cuted: cuted.sty 2021/10/04 v2.0 Mixing onecolumn and twocolumn modes. See the last figure.


The disappearing act

Try this code. (just added a dummy text to check the wide behavior)
Compiled with
This is pdfTeX, Version 3.141592653-2.6-1.40.22 (MiKTeX 21.3) (preloaded format=pdflatex 2021.10.12)
and
memoir.cls 2021/03/23 v3.7o configurable book, report, article document class
and also
memoir.cls 2021/06/16 v3.7p configurable book, report, article document class
cuted.sty 2012/10/04 v1.5 Mixing onecolumn and twocolumn modes
\documentclass[
twocolumn,
]{memoir}
\usepackage{cuted}
\usepackage{kantlipsum}% dummy text
% \usepackage{etoolbox}
% \AfterEndEnvironment{strip}{\leavevmode} % https://tex.stackexchange.com/questions/264510/unexpected-behavior-of-cuted-strip
\setcounter{tocdepth}{3}
\setcounter{secnumdepth}{3}
\begin{document}
\tableofcontents
\chapter{First}
0. \kant[9]
\begin{strip}
\section{Section 1}
1. \kant[1]
\end{strip}
\section{Section 2}
- \kant[2]
\begin{strip}
\section{Section 3}
3. \kant[3]
\end{strip}
\subsection{Subsection 4}
- \kant[4]
\begin{strip}
\section{Section 5}
5. \kant[9]
\end{strip}
- \kant[6]
\end{document}
Output in the .log file by adding \listfiles before \documentclass{
*File List*
memoir.cls 2021/06/16 v3.7p configurable book, report, article document class
iftex.sty 2020/03/06 v1.0d TeX engine tests
mem10.clo 2008/01/30 v0.3 memoir class 10pt size option
array.sty 2021/04/20 v2.5e Tabular extension package (FMi)
dcolumn.sty 2014/10/28 v1.06 decimal alignment package (DPC)
delarray.sty 2014/10/28 v1.01 array delimiter package (DPC)
tabularx.sty 2020/01/15 v2.11c `tabularx' package (DPC)
textcase.sty 2019/09/14 v1.00 Text only upper/lower case changing (DPC)
mparhack.sty 2005/04/17 v1.4 (T. Sgouros and S. Ulrich)
cuted.sty 2012/10/04 v1.5 Mixing onecolumn and twocolumn modes
kantlipsum.sty 2019/07/23 v0.8 Generate text in Kantian style
expl3.sty 2021-02-18 L3 programming layer (loader)
l3backend-pdftex.def 2021-03-18 L3 backend support: PDF output (pdfTeX)
xparse.sty 2021-01-09 L3 Experimental document command parser
xparse-2020-10-01.sty
***********