Freron MailMate

I've MS account (@live.com), being using that for years. A week ago or so it started to show "login error" problem dialog. I've regenerated app-specific password, but it still shows it. After I press "OK" there, it works for a while, until the error shows again.

Here are connection logs (look for the "Error: Server response: “C1 NO LOGIN failed.”" part, that is the message that bugs me):

03:51:36 S: * BYE Microsoft Exchange Server IMAP4 server signing off.
03:51:36 S: R16 OK LOGOUT completed.
03:51:36 Clearing connection to outlook.office365.com
03:51:36 Completed action (3). Observed read/write timeouts: 8/8

03:51:36 Handling reply
03:59:34 Running action
03:59:34 Handling request
03:59:34 Ready to run action (type: 1002, retry count: 0)
03:59:34 Synchronizing mailbox: Junk
03:59:34 Selecting mailbox: Junk
03:59:34 Clearing connection to outlook.office365.com
03:59:34 Trying to connect to outlook.office365.com on port 993 (CFNetwork) without STARTTLS (required)
03:59:34 Resolved hostname (outlook.office365.com).
03:59:34 Prepare secure connection...
03:59:34 Successful connection.
03:59:34 Initiating secure connection...
03:59:34 Returned (4)...
03:59:34 Protocol version: kTLSProtocol12
03:59:34 S: * OK The Microsoft Exchange IMAP4 service is ready. [QgBMADAAUABSADAANQBDAEEAMAAwADEAOQAuAG4AYQBtAHAAcgBkADAANQAuAHAAcgBvAGQALgBvAHUAdABsAG8AbwBrAC4AYwBvAG0A]
03:59:34 C: C0 CAPABILITY
03:59:34 S: * CAPABILITY IMAP4 IMAP4rev1 AUTH=PLAIN AUTH=XOAUTH2 SASL-IR UIDPLUS MOVE ID UNSELECT CHILDREN IDLE NAMESPACE LITERAL+
03:59:34 S: C0 OK CAPABILITY completed.
03:59:34 Reusing latest used password
03:59:34 C: C1 LOGIN ••••••••••
03:59:37 S: C1 NO LOGIN failed.
03:59:37 Error: Server response: “C1 NO LOGIN failed.”. Command attempted: “C1 LOGIN ••••••••••”.
03:59:37 Retrieving password (keychain or user request)
03:59:45 C: C2 LOGIN ••••••••••
03:59:50 S: C2 OK LOGIN completed.
03:59:50 C: C3 CAPABILITY
03:59:50 S: * CAPABILITY IMAP4 IMAP4rev1 AUTH=PLAIN AUTH=XOAUTH2 SASL-IR UIDPLUS MOVE ID UNSELECT CLIENTACCESSRULES CLIENTNETWORKPRESENCELOCATION BACKENDAUTHENTICATE CHILDREN IDLE NAMESPACE LITERAL+
03:59:50 S: C3 OK CAPABILITY completed.
03:59:50 C: C4 ID ("name" "MailMate" "version" "r5937" "vendor" "Freron Software" "contact" "mm-imap-id@freron.com")
03:59:50 S: * ID ("name" "Microsoft.Exchange.Imap4.Imap4Server" "version" "15.20")
03:59:50 S: C4 OK ID completed
03:59:50 C: C5 SELECT Junk
03:59:51 S: * 0 EXISTS
03:59:51 S: * 0 RECENT
03:59:51 S: * FLAGS (\Seen \Answered \Flagged \Deleted \Draft $MDNSent)
03:59:51 S: * OK [PERMANENTFLAGS (\Seen \Answered \Flagged \Deleted \Draft $MDNSent)] Permanent flags
03:59:51 S: * OK [UIDVALIDITY 285] UIDVALIDITY value
03:59:51 S: * OK [UIDNEXT 69] The next unique identifier value
03:59:51 S: C5 OK [READ-WRITE] SELECT completed.
03:59:51 C: C6 NOOP
03:59:51 S: C6 OK NOOP completed.
03:59:51 Performing full synchronization.
03:59:51 C: C7 UID FETCH 1:68 (UID FLAGS)
03:59:51 S: C7 OK FETCH completed.
03:59:51 Completed action (1002). Observed read/write timeouts: 8/8

03:59:51 Handling reply
03:59:51 Running action
03:59:51 Handling request
03:59:51 Ready to run action (type: 1002, retry count: 0)
03:59:51 Synchronizing mailbox: Outbox
03:59:51 Selecting mailbox: Outbox
03:59:51 C: C8 SELECT Outbox
03:59:51 S: * 0 EXISTS
03:59:51 S: * 0 RECENT
03:59:51 S: * FLAGS (\Seen \Answered \Flagged \Deleted \Draft $MDNSent)
03:59:51 S: * OK [PERMANENTFLAGS (\Seen \Answered \Flagged \Deleted \Draft $MDNSent)] Permanent flags
03:59:51 S: * OK [UIDVALIDITY 13] UIDVALIDITY value
03:59:51 S: * OK [UIDNEXT 1] The next unique identifier value
03:59:51 S: C8 OK [READ-WRITE] SELECT completed.
03:59:51 C: C9 NOOP
03:59:51 S: C9 OK NOOP completed.
03:59:51 Performing full synchronization.
03:59:51 Completed action (1002). Observed read/write timeouts: 8/8

03:59:51 Handling reply