Sometimes it may depend on the connectivity of the level your internet. A while ago I had a lot of problems with internet and like you, my games often crashed.
The easiest thing is to check your connection and make sure you are getting a strong signal.
On Xbox 360 to check your connection just follow this link:
Troubleshoot Xbox 360 connection to Xbox Live
While it's a lot to read it will help you in the long run.
To check your speed on Xbox Live go here
Slow experience on Xbox Live (for Xbox One)
You can also check out to see if Xbox Live may be the problem. By going to this link.
Xbox Live Status
The next thing, try replacing your router, when I bought my new router my problems stopped. You can also upgrade to a newer modem to DOCSIS 3.0. This of course depends on your internet speed. If you are below 20mbs I wouldn't worry about upgrading just yet. But upgrading never hurts. However, if you are trying to get 50mbs or more DOCSIS 2.0 bottlenecks. While I am no expert on modems. I think the DOCSIS 2.0 modem bottlenecks around 38mbs.
To Check your speed on the internet, this is the site most people go to.
Speedtest net by Ookla The Global Broadband Speed Test
Use whichever server you wish. I usually do multiple ones to see how it differs.
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