It's because the part of the sentence after the comma is talking about what he is doing "while he cries and panics". This is another way to say the sentences. (He cries and panics when his mother leaves his sight. When he cries and panics, he is suspecting she might leave him again.) Does that make sense?

After the verb which expresses some feelings a GERUND is generally used. (cry, panic). Ex.: I do not like TRAVELLING alone. We enjoyed SWIMMING in the river. She resents his BEING late...

The word 'suspecting' is a present participle. ( NOT a gerund). If you want to check on the grammar, you can look up the term 'participle clause'. This is what the British Council says about them: Participle clauses are a form of adverbial clause which enables us to say information in a more economical way. We can use participle clauses when the participle and the verb in the main clause have the same subject. For example: Waiting for John, I made some tea. https://learnenglish.britishcouncil.org/en/quick-grammar/participle-clauses It's a neat and economical way of expressing a number of ideas in the same sentence. Here's another example: Su.Ki typed an answer to the italki question, hoping that Maggie would find it helpful.