"Red" wrote

Since I moved in to new home in 2004, we have had roof shingle problems

New to you or a new built house and you are first owner? BIG difference.

Today, we had a storm and now I can see a dozen or so loose shingles
flapping up and down. Last year I was told it was last time they would
repair the shingles on my roof. The forman and all but said the shingles
are a bad batch as the same is happening to other homes where the roofs
were put up around the same time as mine. So should I push for a complete
new roof?

You can try, but the difference is it a new to 'you' house or literally a
new one?

No one addressed if this was just 'new to you' (AKA 'new house') but 15 or
more years in age where a roof job was apparently done to re-shingle it.
The roofer is not liable if you have structural issues in a case like that
(such as plywood going bad).