I had the same issue earlier. So I use passport information instead of place of birth and managed to find it. Probably the City/town of birth info was not accurate for me.
The info I use for linking is below.
Tell us about the application section
What program did you apply for?
Category - Permanent Residence
Sub-category - Quebec-Selected Skilled Worker
Application details
Please select one - Unique Client Identifier (UCI) and Family Name
UCI -
Family Name -
Applicant's personal information section
Place of Birth - leave it blank
Passport - Fill up all info
Other Application Information section
Province - Quebec
City/Town/Village - As per application form
Current marital status - As per application form
Number of family members that are part of this application - As per application form
Please try.