The letter states that the effective date for S-Corp is Jan 1 2018 and that the other years were not accepted because she did not file in a timely manner (which she didn’t) she filed in 18. Also she said she did not receive the taxes back for those years. I’ve never had this happening and people did same as her. I don’t know. She said she refaxed the 2553 form.

You can appeal the decision citing your reliance on the applicable Rev Rul. I have had several rejects because IRS didn't follow/acknowledge the Rev Rul procedures. I have ended upo getting the S election approved.

Do you think that by her re-faxing 2553 form she might have another outcome depending on the person handling the form?
I have never done any appeals pertaining to the rejection of a 2553 so I do not know where to start.

I write a letter saying why I disagree with the rejection.

What was written on the 2553 for the "Reasonable Cause" for not filing on time?

This is what they said:
"We have received your form 2553...
Our records indicate your request to be treated as an S corp for income tax purposes, was accepted effective Jan 1 2018.
Your form 2553 wasn't accepted for the requested effective date under the revenue procedure.  In order to qualify, form 1120s for the tax year requested and all subsequent years must be timely filed.  Our records indicate your 1120s forms were not timely filed.
You don't qualify for relief under any revenue procedure; therefore you can apply for a private letter ruling.  .....
That's about it, the letter goes on about tax obligations, etc but they are generalized and not specific to this person.

Were the 2016 and 2017 1120S timely filed?

No, they were not.  They filed both in 2018.  Only 16 was not.

What was written on the 2553 for the "Reasonable Cause" for not filing on time?

I apologize, I misunderstood your question.  It said "president neglected to file in a timely manner"

I highly suspect that is the problem.

That seems to indicate he just didn't get around to filing it, which is NOT a "Reasonable Cause".  If it was something like "President thought the election was already timely filed and upon realizing it was not filed, is now immediately filing it" WOULD be Reasonable Cause.

If the S election was rejected, that makes the entity a corp.  Corporations file 1120 returns, not schedule Cs.

It makes the entity a corp if it was a corp to begin with. If it was a SMLLC electing on a 2553 that was rejected, it may still be a SMLLC. I'm not sure.

I believe you are correct.