Employment pass rejected more than once

Hey guys, just looking for a bit of advice if anyone has been through a similar situation:

Moved to SG almost a year ago for defacto partner's transfer, all very exciting to be expats again and experiencing life in Asia.

I am a recent graduate (end of last year) from a reputable uni back home and was quickly offered a job with a local company based on my education - a degree which is very specific to the role and not offered in Singapore.  Jobs in my area are fairly limited in Singapore as it is an emerging field, and the skills required for the role were very specific.

Initial application for a Q1 pass was turned down, along with three other applications and appeals done over the course of this year.  Extremely frustrated as MoM do not give reasons behind their decision making process and rejection. 

The company that has offered me the job have been fantastic and supportive during this whole process, but have now admitted there is nothing more they can do.  The job was re-advertised and no local applicants fit the skill-set required, however MoM still do not see that I am not only ready and willing to work, but also qualified for the position. 

I realise that my lack of experience does not help my case, but does anyone have any advice or tips on what to do next?  Is it likely that the high number of rejections will have an affect on any positions/EP applications I go for in the future?

Any help will be much appreciated as we are getting desperate and may have to consider leaving Singapore if I am unable to work.

Cheers.