Looking on the internet deeply has found these results:

for quite a long time is the most popular phrase on the web.

for a quite long time 189,000 results on the web	for quite a long time 11,570,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	Tom managed a small bar near Boston for quite a long time. As it is not possible to adopt such a comprehensive approach by means of this directive, and as this directive fixes the level of fuel taxes for quite a long time, this draft opinion includes an amendment proposing a new article relating to review. Isn't it strange how you can know someone for quite a long time and never quite... My father has been a poacher for quite a long time. As Parliament's rapporteur, I have had the opportunity to monitor this matter for quite a long time. He treated her for quite a long time. This directive fixes the level of excise for quite a long time. He's been a cheerleader for quite a long time.

for a quite long time

189,000 results on the web

for quite a long time

11,570,000 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

Tom managed a small bar near Boston for quite a long time.
As it is not possible to adopt such a comprehensive approach by means of this directive, and as this directive fixes the level of fuel taxes for quite a long time, this draft opinion includes an amendment proposing a new article relating to review.
Isn't it strange how you can know someone for quite a long time and never quite...
My father has been a poacher for quite a long time.
As Parliament's rapporteur, I have had the opportunity to monitor this matter for quite a long time.
He treated her for quite a long time.
This directive fixes the level of excise for quite a long time.
He's been a cheerleader for quite a long time.