Mostly I have no problems with sending or receiving mails with osTicket. My experience is when such an problem occurs is that something has changed or prevents access to the mail server:
1) Hoster switches PHP version because of end of life, new PHP version behaves different with software code, email setup settings must be adjusted
2) Hoster has setup a security rule that prevents access to the mail server (could depend on how the software is working) and hoster must allow access
3) Firewall or SELinux rule prevents access to the mail server and must be adjusted to allow the used software to connect
4) Missing PHP extensions, extensions must be installed and activated
5) Hosted mail services like gmail or office 365 or iCloud could have higher security conditions, conditions must be lowered via their webinterface or special conditions must be fulfilled like a connector, or a application aware password