I had a pair of SL-8's and currently have a pair of SL-10's with the speed lace system and have never had an issue with either of them so i would consider your situation atypical.
I did find some references for replacing a broken speed lace - this one has step-by-step instructions:
oneballjay: How to lace the Burton Speed lace boots in 10 min.
From what I've been able to gather, if you order the new lace from Burton they will send you a tool that helps in the repair but I guess you'd need to contact rider services to double check.
Good luck man.