applying LTSVP for my mom

You can apply for an LTVP for your mom if your salary is above S$8000/month.
http://www.mom.gov.sg/foreign-manpower/ … fault.aspx

well I don't have that much salary. Its close to 8k. Is there any other option, otherwise its very hard for her to stay alone as she is totally dependent on me.

what is the duration of a short term visit.

There is no other long-term option.
SVP (i.e. normal tourist visa) is given for up to 89 days and (although there is no hard and fast rule) generally a stay of similar length outside the country is required before re-entry.

Oh Good God.. I have no place to leave her.. perhaps I will try and make a special request also provide my father death certificate to make them believe there is no one to support her back home.. WIll post back here when I get the Visa. wish me luck..

Sorry, the authorities here do not bend rules for your or anybody else's private benefit. Don't put your hopes on this!
I can understand your disappointment, but you will have to find an alternative solution (e.g. rasing your salary to S$8000, or moving to a place that is more welcoming to dependent elders, which Singapore unfortunately sees as unwanted ballast).