well you have maxed out on the repeats. However I don't think that FAS will ever stop offering repeats once there is a backed up reason for them. If you had an employer in Ireland you could get them to write you a letter for another repeat attempt, although I'm fairly sure that you must have done this for the 4th repeat, as the forth requires a letter from the employer. However, if you have something to back up a reason why you may have failed on one of the attempts FAS will listen to you, they always do.
As the above post suggests give FAS a ring, but have some good excuses ready for a couple of the repeat failures, use the stuff that was out of your hands be honest but have some paperwork for them for example a sickness backed up by a doctors letter etc will do the trick.
Are you based in Ireland? if so there is a scheme to try to get some of the phase 7 lads over the line so that they can have a qualification. Worst thing you can do is to just ring them up unprepared.
Best of luck, there are grinds as mentioned before, and FAS will point you in the right direction.