@Justin, sorry for not answering the question earlier. Reason I suggested removing the co-requisites is that sometimes those co-requisites may be the problem and not the specific tweak or app itself. Similar to a corrupted download, your tweak or app won't run properly if the co-requisites are corrupted and can cause problems.
@iMaNoob, I would recommend restoring to a clean copy of iOS 6.1 and rejailbreaking, because I've yet to see a situation like this. I've been asking my colleagues to drop by with their devices and none of them are having any issues aside from their tweaks or apps not working from incompatibility issues or they can't download certain apps/tweaks because of traffic. None that results in the loss of icons from switching Springboard pages. Backup your device, restore and rejailbreak and this time, install the apps/tweaks excluding the one that caused you trouble. Just out of curiosity, which tweak/app did you download to come to this issue since I don't recall you mentioning it at all in this thread.