Do they have a bit of irregular shape? Quite possibly it is the dirty / faulty suppressor. Is it Dionex? They have instructions on how to resurrect it using H2SO4. Otherwise, it just needs to be replaced.

It sounds like you're getting double peaks, sometimes referred to as 'fronting.' Here are some simple solutions: https://www.chromatographytoday.com/news/columns-and-accessories/37/breaking_news/what_is_peak_fronting/31490/

If not check out these clarifying questions for troubleshooting the problem:

1. Are your colleagues running samples that are expected to be in the same range as your samples for sulfate?

2. Are they running those samples on the same machine?

3. Are your colleagues' samples diluted to the same factor as your samples?

4. Have you gotten normal peaks from this machine at this eluent concentration before now - did this suddenly start happening?

 If your answers to the above questions are Yes, No, Yes and No (respectively), then I would suggest playing around with the eluent concentration on your machine before attempting a column flush (referred to above using H2SO4), or buying a new suppressor.  

You could try the following:

Replace the eluent you currently have in the IC with a 5-10% lower or higher concentration and see if that singles out the peak - if it helps, you're on the right track, if not try raising or lowering the concentration in the other direction

(e.g. say you increased the eluent concentration by 5% and it helps, then you keep increasing concentration until it looks sharp and single. If, however, it makes the issue worse, then decrease your original eluent concentration by 5% and see if that helps).

You can change the concentration more than 10% from the original eluent concentration just to be sure - BUT MAKE SURE YOU DON'T GO TOO FAR. Your specific machine/setup will have outline limits for what the system and/or column can take. 

If your answers to the above are Yes, Yes/No, Yes and Yes/No, then there may be an error in your sample preparation that is introducing sulfate into your samples. 

5. Are the other ions you're running coming out similar to your colleagues'?

OR are the other ions coming out as they are expected to, or previously have?

 If yes, then it doesn't sound like the suppressor is the problem. All of the ions are susceptible to suppressor malfunction, and you would see that. 

I've attached some helpful links for your reference:

http://www.nestgrp.com/pdf/Zp1/Sp1/ION_Manual.pdf

http://www.chromatographyonline.com/peak-fronting-column-life-and-column-conditioning-ryan-d-morrison-and-john-w-dolan

http://www.chromatographyonline.com/peak-shape-problems

http://www.ncbi.nlm.nih.gov/pubmed/25456596

Thank all you very much for the links and the advice. I will try the above mentioned steps and get back to you if the fronting continues.