This might not have a purely objective answer. For example:
Most people lose the ability to digest milk by their teens. A few thousand years ago, however, after the domestication of cattle, several groups of people in Europe and Africa independently acquired mutations that allow them to continue digesting milk into adulthood. Genetic studies show there has been very strong selection for these mutations, so they were clearly very beneficial.
Most biologists would see this as a gain in information: a change in environment (the availability of cow’s milk as food) is reflected by a genetic mutation that lets people exploit that change (gaining the ability to digest milk as an adult). Creationists, however, dismiss this as a malfunction, as the loss of the ability to switch off the production of the milk-digesting enzyme after childhood.
And if you go read a review paper on beneficial mutations (as opposed to a popsci article), it never gets to the topic of information loss/gain. The latter seems to be most a concern for creationists (and those debunking their silly claims).
The closest thing that is of concern to biologists is whether a mutation causes a loss or gain of function of the affected protein. There exist ways to score a mutation as gain-, loss-, or switch of function.
I also note that you've substantially edited your question (toward an emphasis on whether that issues invalidates the theory of evolution) after I answered it. As a brief and obvious addendum: no, the argument doesn't invalidate the theory of evolution.
After some searching I found that the argument in question has been put forth by Lee Spetner. Dembski has a somewhat similar argument but not exactly this one. Anyway there seems to be countless variations to it:
An especially good example of silliness is the ID assertion that natural processes cannot create new genetic information. ID advocates have recently been pushing this line heavily as of late (Meyer 2009), even in the science standards of some states (see Matzke and Gross 2006, for discussion and refutation of the information argument), and in the ID movement’s new textbook, Explore Evolution (Meyer et al. 2007). Interestingly, this talking point, at least in the form of a seemingly technical chemical/mathematical conclusion (there are older, more informal versions throughout the creationist literature), was invented in the 1984 proto-ID book The Mystery of Life’s Origins (Thaxton et al. 1984), as a modified version of the creation scientists’ Second Law argument (Matzke 2009). It has since grown into one of the top two or three arguments made by ID advocates.