Hi Chris,
Yes, it's possible I'd say.
I'm a greedy
and have done the aptitude tests three times; in 2010, 2012 and 2014 (about a month ago).
My scores were 123, 118 (with a failed CLAN therefore an overall fail) and then 139 most recently.
When I first took them in 2010 I was very naive and basically turned up with no practice whatsoever (literally nil) and gave it my best shot; I even remember being a bit 'meh' when I was told I had passed. Therefore, when I retook them in 2012 I adopted the same attitude and got 118 and failed the CLAN test (the one with the coloured diamonds and mental arithmetic).
So when my third bite of the cherry came around, I was more than determined to score well. I practiced mental arithmetic like a mad-man. There are mobile apps which test you and I did them whenever I had a spare moment. I rehearsed SDT calculations and played video games as much as possible to improve my coordination.
This took about 3 months and it produced a score of 139, which obviously I was delighted with. You could argue I'm not a natural at aptitude but who cares? I got a competitive pass and I know I can do it (just) without practice from the 2010 test.
Good luck, keep trying!