[noun] + に限って [verb (plain)] + [noun (time)] + に限って
に限って means "of all times", "of all people": the speaker complains that something goes wrong precisely in the one case where it shouldn't. It follows a noun – very often a time, built from a clause: いそいでいる急いでいるとき時, かさ傘がないひ日 – and the second half is the annoying thing that happens.
The second half is usually in the non-past, because it is a pattern you keep running into. A single event in the past works too.
After a person, に限って says that this person is the exception: whatever others might do, they would not. The sentence ends in a strong negative such as はずがない or わけがない.
In notices and announcements, に限って can also mean "only, limited to". にかぎり限り is the more usual form for this.
にかぎら限らず, "not only", and とはかぎらない限らない, "not necessarily", are separate grammar points.