I hadn't noticed that, but I still think we should ignore it, along with most other 〜日 terms. The major refs only have the 日〜 forms.
It isn't difficult to look up the characters individually. That's what we expect people to do with most two-country kanji terms. Only a small fraction of all the possible combinations are included in jmdict.

Kotobank's new interface uses 葡日 specifically meaning Portuguese-Japanese [dictionary], which is what prompted the inclusion of this entry.

日米関係	114791
米日関係	1577
---
英日翻訳	11907
韓日翻訳	3732
中日翻訳	2867
葡日翻訳	No matches
---
葡和辞典	53
葡日辞典	28

It's not arbitrary. For these two-character terms, 日 usually refers to the country, and in standard usage 日 comes first (e.g. 日米関係, not 米日関係).
和 is used when referring to the Japanese language, and there's a semantic difference between 和伊 and 伊和 so it makes sense to have both. (A 和伊辞典 is not the same thing as a 伊和辞典.)
日 can also refer to the Japanese language (usually in the context of translation or interpretation), but with the exception of 英日, 中日 and 韓日, 〜日 terms are uncommon.

That seems arbitrary. We have both 伊和 and 和伊, for instance. No harm there.