Can a Japanese omamori be kept as a souvenir after a year without returning it?

If you simply keep it as a souvenir after a year, I think that is acceptable. Not returning it need not make you assume something will go wrong. First distinguish whether you want continued protection or treasure a memory of travel and worship.

I have discussed the Japanese custom of replacing omamori after a year within local culture and belief. If you want continued protective use, learn what the original shrine recommends. Religious tokens from every place do not all have identical durations and care methods.

For a collection, store it properly instead of leaving it anywhere. From religious experience, something used as an energetic object still deserves care, but I also said most simple souvenir collecting would not have any particular effect. If something genuinely seems unusual, understand the situation then, rather than deciding every old omamori has become harmful. Overseas purchases cannot necessarily be returned annually. If you like it, keeping it carefully as a souvenir is fine.