When should I see a doctor about my baby's sleep problem?

The earlier the better. You want to rule out any physical ailments that could be preventing your child form sleeping. 
The first thing to consider is if they are teething.  This can often cause excessive crying and problems sleeping at night.  
Trouble sleeping could also be caused by reflux. When babies lie down they can have severe reflux and become quite restless (reflux is often referred to as colic).
Your baby could be suffering from something more serious, like breathing problems (apnea), neurological problems (like seizures) or cardiac issues (rare but possible).
If these physical problems are ruled out, take a look at their sleep regimen, scheduling, and eating schedule.

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Important: This content reflects information from various individuals and organizations and may offer alternative or opposing points of view. It should not be used for medical advice, diagnosis or treatment. As always, you should consult with your healthcare provider about your specific health needs.