@acer 

Thanks for the elaborate answer and analysis. I tried looking into the LinearMultivariateSystemInternal routine, but could not make head nor tail of the code. Partly because I did not know a way of doing modifications to a protected routine in Maple. But the Plots:-inequal seems to be correct to me. And I think that it makes sense to convert all '<>' relations to alternate form. And it worked for my code. Also I guess, a crude and not-so-exact way to verify for my application is to look for integer points within the solution space for both the approaches. Beyond the integer points, I am not sure how to verify, either, as it will be a set of regions in both the cases and those might not be mapped one-to-one.

But I am not sure if it is a good idea to modify the routines to do it in production? I mean part of this code will be a part of my research code that I might have to publish in future. I am curious to know why is this issue though, I mean is it a bug in the routine or like an untested scenario ? Or is this by design. 
But for my current purpose, I can go ahead with the approach outlined by @Kitonum in his response. The Integerpoints1 procedure works like a charm. 
 

@Kitonum Thanks for the procedure. Actually, that solves my problem and the performance is quite good. Hence I am going to use the code. 
But sadly I selected acer's answer as the best answer as his answer helped me understand the issue with the Maple's SolveTools package as well  as with a valid solution. If I could I would select your answer to be as much helpful as acer's answer. :) 
Thanks again. 
 

@vv Thanks for the help. I appreciate it. And the decomposition is indeed quite large. But I am going to have to solve it for integral solutions. I guess I can use something like isolve then? This seems like an approach that can still work. Will try it out though as you said, speed of computation needs to be considered in reality as this is still a smaller set, for I am going to have to work with even bigger system of inequalities if I put this as a generic code. :) .

Also, I have found PolyhedralSets to be a little slower as compared to the alternate Convex package that I am using.
http://www.math.uwo.ca/faculty/franz/convex/doc/current/index.html . 
E.g. minkowski sum is much slower using PolyhedralSets as compared to minkowski sum in convex package.