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Hi Marco.

I would suggest to meet your grassroot MP, talk to them and tell them of Yr situation. They will listen to you and write an email to ICA. The email is not sent to a general enquiry which the public can access to. So it'll get special attention and hopefully a positive reply either via letter mail or call. Usually within 2 weeks or a month. Its the best option in my opinion.

Zedzef: I have not heard of any example where an MP letter helped a foreigner getting a visa - and only very few where the MP did actually agree to write such a letter at all. Their allegiance is with Singaporeans (who vote for them), not foreigners.

Marco: You can only apply for an LTVP for your wife (legally married).
If she is not your wife (what does "spouse in law" mean?), she cannot get a visa from you, because Singapore does not recognise other kinds of partnership.
If she is your wife, contact ICA and ask for an explanation why she was rejected. An appeal can only be successful if you address the rejection reason.

Actually ICA accept spouse in law status - I am French and the French Authorities are legally recognising Sppuse in law status when unmarried couple lives together - I provided this certificate to ICA ( and many French working in singapore under EP obtain visa forbtheir partner with the same document)
I will appeal , but ICA wont provide reason for rejection

I never heard the term „spouse in law“ and also cannot find anything about it on the Internet.
If it is some kind of registered partnership legally equivalent to a marriage and if your home country recognises it and provides the required paperwork, then yes, Singapore must in principle recognise it, too (by international treaty). But they don‘t like this and often create problems - predominantly for same-sex couples.

Clear her tax. That's most probably  the reason

Spouse in law is recognised in Singapore.  If French government  recognises it legally then Singapore  will too. That's not the problem