I have had the same problem with some of my FIFA games. In FIFA 07 I started with Legia Warsaw, a 3 star team with a budget of 5 million euros. By the 13th season I had won 13/13 League titles (smashing every team with quick simulation such as Lodz 11-0) 10/13 league cups, one champions league title and one European super cup. I had made them into a 4 and a half star team with a budget of 150 million.
Another manager mode I did with FIFA 07 was with Juventus. They were a 4 star team with a budget of 70 million euros. I won 1 serie B title, 3 serie A titles, 5 coppa nazionale titles, 4 super coppa nazionale titles, 3 champions league titles and 2 European super cups all in just 7 seasons.
In FIFA 09 I used Charlton Athletic and I won 2 championships, 3 premier league titles, 3 FA cups, 3 Champions league titles and 2 European super cups in just 7 seasons.
In FIFA 10 I used Newcastle and I won 1 championship, 7 Premier League titles, 4 FA cups, 1 League cup, 1 Europa League title and 3 Champions League titles in 10 seasons.
In FIFA 12 I used Basel and I won 9 Swiss Super League titles, 7 Swiss cups and 2 semi-final appearances in the champions League, in 9 seasons.
In FIFA 13 I used Basel and I won 7 Swiss Super League titles, 6 Swiss Cups and a Europa League title, In 7 seasons.
I also used Bayer Leverkusen and I didn't win any League titles but I had 3 3rd place finishes and 1 second place finish and I won 2 German cups In 4 seasons.
In all these career modes the game froze and did not let me pass a certain date.
I have now found a way around this in the new career modes try your best not to have too many players, have 32 at the very most and not too many players in your youth academy. Try to also have two save files of the game so if one freezes then use the other.
I am currently using Legia Warsaw in FIFA 13 and I have won 9/9 League titles, and 8/9 League cups, with a semi-final appearance in the Champions League. I am mostly using Youth Academy Players.