How to fix Gmail that won't get new messages from IMAP server

My wife has a cheap oangcc android tablet bought from Amazon. She uses it to check her email on Google, and on a local Cyrus- IMAP server. It has worked fine for years, but now won't collect new mail from the local imap server. It says it is synching, the whirly thing comes up for a short time, but new mail doesn't arrive. The local server has a self-signed certificate. The IMAP settings are port 143 and STARTTLS (accept all certificates). If I use a different android device, it all works fine. If I delete her email account on the tablet, and re-create it, it gets all the email OK. But then, after a short while, new emails aren't collected any more. I even tried deleting the gmail data and cache, and recreating the account. The problem still came back. I have turned on logging for her mailbox on the cyrus server, and it is having conversations with the server. I can't see anywhere where it is asking to download mail from her inbox. The conversations from an attempt to sync from her tablet are:

>1691229516>5 OK [CAPABILITY IMAP4rev1 LITERAL+ ID ENABLE ACL 
RIGHTS=kxte QUOTA MAILBOX-REFERRALS NAMESPACE UIDPLUS 
NO_ATOMIC_RENAME UNSELECT CHILDREN MULTIAPPEND BINARY CATENATE 
CONDSTORE ESEARCH SORT SORT=MODSEQ SORT=DISPLAY 
THREAD=ORDEREDSUBJECT THREAD=REFERENCES ANNOTATEMORE LIST-
EXTENDED WITHIN QRESYNC SCAN XLIST URLAUTH URLAUTH=BINARY X-
NETSCAPE LOGINDISABLED AUTH=PLAIN COMPRESS=DEFLATE IDLE] User 
logged in SESSIONID=
1691229516>* CAPABILITY IMAP4rev1 LITERAL+ ID ENABLE ACL 
RIGHTS=kxte QUOTA MAILBOX-REFERRALS NAMESPACE UIDPLUS 
NO_ATOMIC_RENAME UNSELECT CHILDREN MULTIAPPEND BINARY CATENATE 
CONDSTORE ESEARCH SORT SORT=MODSEQ SORT=DISPLAY 
THREAD=ORDEREDSUBJECT THREAD=REFERENCES ANNOTATEMORE LIST-
EXTENDED WITHIN QRESYNC SCAN XLIST URLAUTH URLAUTH=BINARY X-
NETSCAPE LOGINDISABLED AUTH=PLAIN COMPRESS=DEFLATE IDLE
6 OK Completed
1691229516>* NAMESPACE (("INBOX/" "/")) (("user/" "/")) (("" 
"/"))
7 OK Completed
1691229516>* STATUS INBOX/Sent (UIDVALIDITY 1392197170)
8 OK Completed
1691229516>9 OK Completed
1691229517>* 1875 EXISTS
* 0 RECENT
* FLAGS (\Answered \Flagged \Draft \Deleted \Seen $Forwarded)
* OK [PERMANENTFLAGS (\Answered \Flagged \Draft \Deleted \Seen 
$Forwarded \*)] Ok
* OK [UNSEEN 1] Ok
* OK [UIDVALIDITY 1392197170] Ok
* OK [UIDNEXT 2030] Ok
* OK [HIGHESTMODSEQ 1741] Ok
* OK [URLMECH INTERNAL] Ok
10 OK [READ-WRITE] Completed

>1691229517>* SEARCH
11 OK Completed (0 msgs in 0.010 secs)
)
>1691229517>* SEARCH
12 OK Completed (0 msgs in 0.010 secs)

>1691229530>5 OK [CAPABILITY IMAP4rev1 LITERAL+ ID ENABLE ACL 
RIGHTS=kxte QUOTA MAILBOX-REFERRALS NAMESPACE UIDPLUS 
NO_ATOMIC_RENAME UNSELECT CHILDREN MULTIAPPEND BINARY CATENATE 
CONDSTORE ESEARCH SORT SORT=MODSEQ SORT=DISPLAY 
THREAD=ORDEREDSUBJECT THREAD=REFERENCES ANNOTATEMORE LIST-
EXTENDED WITHIN QRESYNC SCAN XLIST URLAUTH URLAUTH=BINARY X-
NETSCAPE LOGINDISABLED AUTH=PLAIN COMPRESS=DEFLATE IDLE] User 
logged in SESSIONID=
1691229530>* CAPABILITY IMAP4rev1 LITERAL+ ID ENABLE ACL 
RIGHTS=kxte QUOTA MAILBOX-REFERRALS NAMESPACE UIDPLUS 
NO_ATOMIC_RENAME UNSELECT CHILDREN MULTIAPPEND BINARY CATENATE 
CONDSTORE ESEARCH SORT SORT=MODSEQ SORT=DISPLAY 
THREAD=ORDEREDSUBJECT THREAD=REFERENCES ANNOTATEMORE LIST-
EXTENDED WITHIN QRESYNC SCAN XLIST URLAUTH URLAUTH=BINARY X-
NETSCAPE LOGINDISABLED AUTH=PLAIN COMPRESS=DEFLATE IDLE
6 OK Completed
1691229530>* NAMESPACE (("INBOX/" "/")) (("user/" "/")) (("" 
"/"))
7 OK Completed
1691229530>8 OK Completed
1691229530>* LIST (\HasNoChildren) "/" "INBOX/Deleted Items"
* LIST (\HasNoChildren) "/" INBOX/Drafts
* LIST (\HasNoChildren) "/" INBOX/SPAM
* LIST (\HasNoChildren) "/" INBOX/Sent
* LIST (\HasNoChildren) "/" "INBOX/Sent Items"
* LIST (\HasNoChildren) "/" INBOX/Trash
9 OK Completed (0.000 secs 7 calls)

>1691229531>5 OK [CAPABILITY IMAP4rev1 LITERAL+ ID ENABLE ACL 
RIGHTS=kxte QUOTA MAILBOX-REFERRALS NAMESPACE UIDPLUS 
NO_ATOMIC_RENAME UNSELECT CHILDREN MULTIAPPEND BINARY CATENATE 
CONDSTORE ESEARCH SORT SORT=MODSEQ SORT=DISPLAY 
THREAD=ORDEREDSUBJECT THREAD=REFERENCES ANNOTATEMORE LIST-
EXTENDED WITHIN QRESYNC SCAN XLIST URLAUTH URLAUTH=BINARY X-
NETSCAPE LOGINDISABLED AUTH=PLAIN COMPRESS=DEFLATE IDLE] User 
logged in SESSIONID=
1691229531>* CAPABILITY IMAP4rev1 LITERAL+ ID ENABLE ACL 
RIGHTS=kxte QUOTA MAILBOX-REFERRALS NAMESPACE UIDPLUS 
NO_ATOMIC_RENAME UNSELECT CHILDREN MULTIAPPEND BINARY CATENATE 
CONDSTORE ESEARCH SORT SORT=MODSEQ SORT=DISPLAY 
THREAD=ORDEREDSUBJECT THREAD=REFERENCES ANNOTATEMORE LIST-
EXTENDED WITHIN QRESYNC SCAN XLIST URLAUTH URLAUTH=BINARY X-
NETSCAPE LOGINDISABLED AUTH=PLAIN COMPRESS=DEFLATE IDLE
6 OK Completed
1691229531>* NAMESPACE (("INBOX/" "/")) (("user/" "/")) (("" 
"/"))
7 OK Completed
1691229531>* STATUS INBOX/Sent (UIDVALIDITY 1392197170)
8 OK Completed
1691229531>9 OK Completed
1691229531>* 1875 EXISTS
* 0 RECENT
* FLAGS (\Answered \Flagged \Draft \Deleted \Seen $Forwarded)
* OK [PERMANENTFLAGS (\Answered \Flagged \Draft \Deleted \Seen 
$Forwarded \*)] Ok
* OK [UNSEEN 1] Ok
* OK [UIDVALIDITY 1392197170] Ok
* OK [UIDNEXT 2030] Ok
* OK [HIGHESTMODSEQ 1741] Ok
* OK [URLMECH INTERNAL] Ok
10 OK [READ-WRITE] Completed

>1691229531>* SEARCH
11 OK Completed (0 msgs in 0.010 secs)
)
>1691229531>* SEARCH
12 OK Completed (0 msgs in 0.010 secs)