Steps
1. First find out what is causing your speed to slow down (lag). This can be cause by....
# The host of the match might be far away from you and it's difficult for you to have great signal strength with someone half-way across the world.
# Somebody might be cheating in the game via lag-switch. Which is a modification of the Xbox Console that can scramble all the other players connection. This voids the warranty of the Xbox and can get you banned from Xbox LIVE. There are more than 100 versions of lag-switches some homemade and some bought from stores (not supposed to be used for this purpose the ones bought for stores are supposed to be used to speed up computer connection but can be solder to the Xbox and be used for the reversed purpose of slowing down others connection and speeding up yours. I will describe the different kinds at the end of the article.
# Just a bad connection this looks similar to a lag-switch however; its really just the host connection has dropped or slowed down causing everybody to have a slow connection but, it will show the host as having full signal strength when they actually don't.
2. Your connection may be slow, or your connection may be set to moderate or strict. This can be changed by turning off your wireless router/unplugging your network connector from Xbox. if this doesn't work than read Change Your Nat Type on Xbox Live.
3. After identifying the problem you can try and boost connection speed.
If the problem is lag-switch related, or host connection problems... then unfortunately there is nothing you can do to fix this.
4. If the problem is your connection then you may need to get a better network connector for your Xbox. You may also have to close out some programs on your computer. As this can slow down connection speed across anything connected to your internet.