Xbox 360 errors try this, you might experience less disconnects.
When you get connectivity errors, you might want to try the following: (If you opened the ports etc)
First close the game
Then go to your harddrive and clear the cache 3 times.
Shutdown your xbox360
Go to your modem and power it off for 10 seconds.
Power it back on.
When it is back online and the lights are blinking normally
Start the xbox and your game again.
This keeps me playing for 60 to 120 minutes.
What I think that happens, is that the cache of the modem is overloaded at some time, because Destiny seems to be using all of the bandwidth. This could be also the case for the Xbox, because I tried to do the steps without the cache cleaning, and I got thrown out after 10 minutes.
I read on the forum that capping Destiny to like 60% of your max bandwidth, is working to get the errors gone.
Too bad my modem can't do this...