Meaning of 危ぶめる

I think you're right that it's not the potential form of the godan verb 危ぶむ. However, the verb 危ぶむ has two forms (from 大辞林):

一（ 動マ五［四］ ）(godan/yodan)
    .....
二（ 動マ下二 ）(shimo nidan)
危ない状態にする。 「国家を－・めんとする物／平家 5」

In particular, the second definition is a shimo nidan verb, which is related to the modern-day ichidan verb. We can look here for how a shimo nidan verb is conjugated:

ている attaches to a verb's 連用形 form, which for this shimo nidan verb would be 危ぶめ. Thus, we would get 危ぶめている, which is the word you saw in your sentence. The word in your sentence comes from definition 2 above.