Looking on the internet deeply has found these results:

many times is the most popular phrase on the web.

many a times 1574,000 results on the web	many times 1274,000,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
Carlo and I have walked the Labyrinth many a time. This vest saved his life many a time. I've tried, miss Morgan, many a time. Many a times, mother would cover her face with the blanket. But I've seen it on television many a time. Got bored hearing it many a times, father. So, June it rains, so many a times all of us would be huddled under the tin roof, waiting for the rain to stop. I've walked to Groby of a Sunday afternoon many a time.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

many a times

1574,000 results on the web

many times

1274,000,000 results on the web

More popular!

Carlo and I have walked the Labyrinth many a time.
This vest saved his life many a time.
I've tried, miss Morgan, many a time.
Many a times, mother would cover her face with the blanket.
But I've seen it on television many a time.
Got bored hearing it many a times, father.
So, June it rains, so many a times all of us would be huddled under the tin roof, waiting for the rain to stop.
I've walked to Groby of a Sunday afternoon many a time.

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