(こんな)時に限って literally means "limited to the time (like this)", but it's a set phrase that means "of all times" or "especially at times like this". It's used when something happenesbad happens at the least convenient moment.
急いでいる時に限って車が故障した。
The car broke down of all times when I was in a hurry.帰ってみる does not mean "to try to return". This is a very common mistake learners make. See: What is the difference between "verb＋て＋みる" and "verb＋(よ)う+とする"?
For this たり, see: Meaning of ーたりしない and What does 良いところだったりする mean in this sentence?
こんなときに限って家に帰ってみるとなかったりするのだ。
Of all times, it's when you're in such a situation that you can't find it after (trying) getting back home.
→ Especially at times like this, it often happens that you return home to find nothing.