Is it closing, or crashing? Try reinstalling the program. https://www.mozilla.org/en-US/thunderbird/

It is not a crash, just a regular closing

try changing the default browser to edge and see if this is still the case. Then change it back and see if that helps. I would say Thunderbird is crashing, not closing normally. Because clicking a link does not close Thunderbird. Please try the following: *Restart Thunderbird with add-ons disabled (Thunderbird Safe Mode). On the Help menu, click on "Restart with Add-ons Disabled". If Thunderbird works like normal, there is an Add-on or Theme interfering with normal operations. You will need to re-enable add-ons one at a time until you locate the offender. *Restart the operating system in '''[http://en.wikipedia.org/wiki/Safe_mode safe mode with Networking]'''. This loads only the very basics needed to start your computer while enabling an Internet connection. Click on your operating system for instructions on how to start in safe mode: [https://support.microsoft.com/en-us/help/12376/windows-10-start-your-pc-in-safe-mode Windows 10], [http://windows.microsoft.com/en-us/windows-8/windows-startup-settings-safe-mode Windows 8], [http://windows.microsoft.com/en-us/windows/start-computer-safe-mode#start-computer-safe-mode=windows-7 Windows 7], [http://windows.microsoft.com/en-us/windows/start-computer-safe-mode#start-computer-safe-mode=windows-vista Windows Vista], [http://www.microsoft.com/resources/documentation/windows/xp/all/proddocs/en-us/boot_failsafe.mspx?mfr=true" Windows XP], [http://support.apple.com/kb/ht1564 OSX] ; If safe mode for the operating system fixes the issue, there's other software in your computer that's causing problems. Possibilities include but not limited to: AV scanning, virus/malware, background downloads such as program updates.

Temporary I made Chrome a default browser, and it worked as before did Firefox. So I uninstall Firefox and have installed it anew. After that, as a default browser, it worked with Thunderbird not closing it it on each click on link in message in Thunderbird. Strange that there is not a place in Settings that controls Firefox behavior with this issue, at least expert replaying me does not mention it.