My husband's ex wife has custody of their 14 yr old son with my husband having visitation. Since September she has left the boy with us for extended periods (up to 2-2 1/2 months at a time) without contacting my husband for 3-4 weeks at a time.While being with us the boy does well in school and has a stable established life style. We would love to have custody of him. So my question is since she has legal custody and leaves him like this, can we claim that she abandoned him and what can we do?

She has not abandonded him, since she knows where he is and arranged for his well being, by leaving him with you.

Now, for a level term, you can file in court, to have custody changed and you (well your husband) to get legal custody, no contact for a few weeks is not really a big issue, but her having son stay with you, may be enough, if the boy will testify he prefers to live with you.
And showing that his grades are better, show grades with her, bad, grades with you good.

Agreed this does not come close to being considered abandonment.

I would strongly suggest that you consult with a local attorney who will know the moods of the courts before you consider filing for a change in custody.