Hi,
This is very common problem to send Email from most of the servers to Microsoft Network. Please ask your hosting server provider for 3-4 IPs on different subnet, once available I'll test them if they are not partly block by Microsoft Network. If any of IP or all new IPs work good, I can configure those IPs in your email configuration to be used to send email to Microsoft Network. Any IP which is found blocked you can discontinue.
There is no other solution to this issue.
I am providing similar support to over 18 hosting companies since last 14 years who trusted me. I can manage any kind of issues in linux/windows/vps and Azure+Amazon+Google Cloud including any code level support in any language, server optimization, firewall, load management etc.
I am dedicated to my work and provide 100% customer satisfaction and on time delivery, you can review my profile and feedback. I also provide support for any issue if required after job is done to retain my clients to get more works and references.
Please let me know if you are interested, I'll be happy to assist in resolving this issue.
Thanks & Regards
Sandeep Verma