Vector formats are not as straight forward things as pixel based formats. In general you can only expect some parts of your designs to transfer well between systems. The most common vector formats that I encounter are (in no particular order):
There certainly are many others. The last four are almost exclusively used by engineers, but ill return to that nuance in a bit. None of these formats are entirely compatible. They vary quite widely in what they can do. Let us make some description of what the formats are for.
PDF is a document format, PDF is designed to preserve fidelity over several systems. But PDf is not a singular format and has many variations which may or may not be understood by the target application.
EPS is a printer programming language, that has been encapsulated for easy embedding in host PostsScript programs. As such it might contain nearly anything from programs that generates barcodces on fly to raytracers. However it is not really intended originally to be a transfer format. It can obviously unpack the drawing routines as primitives, but here's the catch since those primitives may be anything not all of them may work out very well. Second the purpose of EPS is to make pages for print and the language is not so interested anything beyond that. Adobe does not write transparency info into EPS so there's no way to retrieve data that has been removed.(tough see AI below for clarification).
SVG is a format designed to transfer the scene graph as such SVG is probably the best transfer format after PDF. SVG is born out of the need to have truly open and relatively easily understandable format. Mainly because PDF was not open at the time but also because generating PDF by hand is cumbersome. The biggest problems is that SVG has all kinds of unnecessarily features that make it hard to implement properly. EPS and PDF are both pure Adobe designs so they work relatively well with adobe software. SVG works relatively well if, and only if, you account for the differing capabilities. But not only that the complexity of SVG has led to need for light version of SVG.
AI is the proprietary format of Illustrator. The format itself is actually either PDF or EPS (depends on the AI version you save with) with additional information embedded so that Illustrator can reverse the procedure perfectly. As noted above there's several versions of AI all of which do not implement same feature set. Now technically this file can contain everything that AI has. And if you have a AI file you should be working of that.
CDR is the native format of corel draw, and is in general a pain to open in other software. SWF is the format for flash which is also a vector format. DWG trough STEP are common CAD transfer formats, other exotic formats exist. This brings us the the really hard part while theoretically AI, EPS and PDF are capable formats not all vector formats agree even with even the most basic conventions. Cad formats can contain b-Splines winch are a different way of managing splines form Beziers. Mainly because you can not make a perfect sphere with bezier splines and need for higher order derivatives.
What happens when you translate between these systems? Data gets lost, pure and simple. In fact several of the formats were even not designed for data transfer between editing software. So its not a coincidence that they do not play ball really well. There's really nothing you can do unless you limit your capabilities to the least common denominator. Even in this case you should try to let the original authoring software do the conversion or something like a broken phone effect occurs. The software tries to keep fidelity best it can but its just already so far broken that it tries to compensate by rasterizing the result.
To summarize. Most likely you can not do what you ask without actually sacrificing or doing some extra work.
Ammendum: How do you actually solve the problem? Ods are you can not solve the problem. Which is what the entire explanation is. Reasoning is as follows. If the exporter has problems with your file then there may already have happened a substitution to raster graphics and the mask data is lost. If this is the case then the only thing you can do hope is to gain access to the original. If the problem persists even with the original then there's 2 things you can do:
You can remove the offending element. Assuming this is possible off course. Or you can try to modify it to comply with the exporters capabilities.
White your own file with either a custom exporter or manually. In either case you dont have much choice on the matter since the target formats may not support the feature you want to keep. This may or may not work. An offshoot of 2 is to try yet one more tool
So I would suggest the following: Export the target to PDF and try to dissemble it form that. You may be in much more luck than trying to eat the eps file as PDF has more tools that understand any potential transparency.
However there's a really high chance it wont work, end of story. But not having your file or even vaguest idea what it contains makes it impossible to say anything more.