Try this:

• Go to the Help menu and click Troubleshooting Information.
• Click the Open Folder button, next to the Profile Folder entry.
• Close Thunderbird.
• Delete the file global-messages-db.sqlite in the profile folder that just opened.
• Restart Thunderbird and wait for the search index you just deleted to regenerate. (That may be quite a while.)

Also see Rebuilding the Global Database.

Did it help?

The activity manager got stuck with the message "Determining which messages to index in the sent folder" I reduced the size of the message base by deleting and archiving, and the sent folder is now just under 700 messages. Then I tried again. After 20 hours the activity manager still appears to be moving with a live green bar, but with the same message.

Right-click the Sent folder, select Properties and then Repair Folder. Perhaps the index file for the Sent folder has become corrupt. Did you remove the Global Database?

Side note: some Windows 10 users experience better performance when disabling Enable Global Search and Indexer in Options > Advanced panel > General tab.

Do you happen to use the Thunderbird Conversations add-on? If so, you may be suffering this issue. The add-on on addons.mozilla.org does not seem to be fit for TB 52, but a patched version can be found on GitHub, though it will only work in Thunderbird Daily builds.

If you don’t use the add-on, could there be another one causing it, i.e. what happens when you run Thunderbird in Safe Mode?

Tonnes said

Right-click the Sent folder, select Properties and then Repair Folder. Perhaps the index file for the Sent folder has become corrupt. Did you remove the Global Database? Side note: some Windows 10 users experience better performance when disabling Enable Global Search and Indexer in Options > Advanced panel > General tab. Do you happen to use the Thunderbird Conversations add-on? If so, you may be suffering this issue. The add-on on addons.mozilla.org does not seem to be fit for TB 52, but a patched version can be found on GitHub, though it will only work in Thunderbird Daily builds. If you don’t use the add-on, could there be another one causing it, i.e. what happens when you run Thunderbird in Safe Mode?

Thank you. Disabling the conversations add-on was the key