ともすれば + [sentence]
ともすれば is an adverb meaning "apt to", "liable to": left alone, things easily slide in a direction, usually a bad one. It goes before the clause it qualifies, and that clause usually ends in がちだ, やすい or てしまう.
The tendency is one to watch out for – forgetting, neglecting, getting emotional – so the sentence often carries a warning. A good tendency does not take ともすれば.
All four belong to writing, editorials and formal speech. In conversation, つい with きごう〜てしまう or a plain きごう〜がち does the same work: ついわすれちゃう忘れちゃう.