NY state-
Can your employer verbally tell you if you are out one more times for whatever reason, you will be terminated? I have a young child with asthma and the company knows this, but continue to give me formal written warnings. If they do terminate me, do I have a legal leg?

Yes, they can, so long as they are not singling you out in comparison to others with similar attendance patterns. Otherwise, you do not have a legal basis of complaint.

If your absence is because of an ill child you may be protected.

"The FMLA requires certain employers to allow their employees to take up to twelve weeks of unpaid leave a year to care for a seriously ill family member, to recuperate from their own serious illness or to take care of a newborn or newly adopted child. In most cases, the employer must reinstate the employee when he or she returns from leave." more information at

http://public.findlaw.com/employment_employer/nolo/ency/BC32DE80-7A04-4E33-AFF1E5291CDB37C9.html

I hope this helps.

Best of luck.