Minimalism as a life style is not synonymous with the art style. Throwing away everything every six months? That's confusion, not minimalism.
A really effective purge can be an empowering act. Suddenly what was once cluttered is now clean by design. What was once complex is now simple. It really feels great to be able to have that binary switch of, first, when that junk accumulates, and second, when that junk is removed judiciously.
However, I maintain that if you are continuously purging, day in and day out, and it never seems to stop the problem, maybe the issue is at the source of the junk, not the junk itself.
Just last year I cleaned out my video game collection, and I removed and sold most of my PC games (barring ones I couldn't technically remove - some DRM-inflicted games cannot be removed from my account). Yet, it seems that over time, I accumulate more and more, forgetting what is important to me and thus, I'm again faced with a shelf of games that I don't really need. Most of these games were $3 or less, and games that legitimately sounded like fun, but in retrospect, the burden imposed on me by their mere existence was more of a cost than the enjoyment I got out of their function.
I'm letting the garbage can do my minimalism for me. But this ignores the fundamental truth of minimalism: just because it looks minimalist doesn't mean it really is. A clean shelf doesn't imply minimalism any more than a clean sink - both we can assume to be in a temporary state of aesthetic minimalism and as such we can never assume that what is clean will stay clean.
How to fix this? Admit there is a problem, naturally. Understand the reason why the problem is a recurring action. Think of ways to solve the problem at its source. Fix it.
Why do I continue to buy PC games? Well, the nature of the market allows me to grab some fancy games on clearance for $5 or less. The drive to buy new games all the time is a habit borne from a saturation within the industry - you get so used to trying new things that, once you've found a handful of games you really like and don't need much else for entertainment, it's still hard to stop buying new games.
How can I solve this problem? Well, ignore the games entirely, and concentrate on a different hobby. Play more of the games I already own to remind myself that I already have enough. Concentrate on negative aspects of the purchase - physical burden, woes with the DRM, etc. Blog about it (yes, this helps me quite a bit - it transforms my fluid thoughts into more solid words and arguments).
And thus, the only step left is to implement the fixes and walk away.