Please help us help you and fill where relevant:
Your LimeSurvey version: 5.3.16
Own server or LimeSurvey hosting: LimeSurvey
Survey theme/template: fruity
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Hello! We have launched our survey and one of our participants tells us they have completed the survey on a tablet but we do not see that they have opened or completed the survey at all. 
All participants receive a personalized link from us, with their token embedded and we send this manually (not through LimeSurvey). 
We have token-based persistent response switched on. 

We are able to see that others have opened and completed the survey just fine. 

Do you all have any ideas why this may be?
Please let me know what other info I should share.

Thanks all!

As there is a new record created in the database as soon as the respondent opens the survey, there are two ideas that come to my mind.

1. The respondent doesn't tell you the truth (Or - to be polite - he was confused because he had answered a different survey)
2. You sent the same link to two persons (you sent manually, so this might happen)

Joffm

I agree with Joffm. As the others work, there is a very high chance that the problem is with the respondent.

As soon as someone opens the survey link a entry in the database is created. If this entry is not created, the respondent can't get to the end of the survey, in my opinion.

To add to Joffm's options:
3. The respondent deleted the response if this options is provided in the survey interface
4. Someone that has access to the limesurvey backend has deleted this answer

If there is really no data in the database for the specific token, my guess would be it is not due to Limesurvey, especially given the fact that others can answer the survey just fine.

What happens if you click on the link that you have sent to this respondent?