I have not had any trouble with my CMG Infinities, but I've run into some issues with a similar design - the ARC AAA.

Check you battery for damage. Is there a dimple in the bottom from that little bump contact in the bottom of the Infinity? I've had batteries continue to work with this dimple, but some have failed. You can put alot of pressure on a battery with the screw-to-turn-on lights, (this is what causes the dimple), to the point of causing battery failure.

Cleaning contacts is highly recommended. Use a pencil eraser to get the bottom of the Infinity tube. Don't forget to clean the threads where the head screws on too. These can get gunk covered as well, and will cause conductivity problems. I just wad up a Kleenix and stick it in there and twist it around myself, but you would go more hard-core with a toothbrush and some alcohol if needed.

Older ARCs also need to have a "roll crimp" put into the head for reliably. Infinities do not need this AFAIK. Maybe others can answer if they have Infinities that require this modification like older ARC AAA's do.