How to prevent transaction log getting full during index reorganize?
Best practice is to REORGANIZE below around 30% fragmentation and REBUILD above this. Simply, REBUILD makes a clean copy, REORGANIZE does it in-situ. 

Check what you're actually doing: you don't have a maintenance plan doing both do you?

On larger tables (50GB table is getting there) I've seen REORGANIZE consume all transaction log space if you follow this rule. Not often: only one system with a certain load pattern. The REORGANIZE just ran until the log expanded and consumed all disk space.

We switched to REBUILD instead with no more problems, but ignored fragmentation below 25%. This worked better for us: you'll have to see if it works for you.

REBUILD may affect the performance more than REORGANIZE in production, but this can sometimes be mitigated with the ONLINE option (Enterprise Edition required).