I have heard many complaints about the Destiny servers booting people and I've experienced it myself. This is not as easily fixed as one might expect. Most people don't actually connect directly to the internet; they connect to the LAN, which can actually be slowed down by internet users across your neighborhood/apartment complex. Also, if you play in the evening, the bungie servers will be worked over a little more than earlier in the day due to players coming home from work and school. To test the difference, try switching to another game online. For me, I switched to Halo: Reach matchmaking and found that I got booted there too, repeatedly. This was some time around 5 on a Friday. You could adjust your schedule to find a better connection time, you could ask bungie to get more servers, but you can't expect them program better connectivity, it doesn't work that way. Also, check your ethernet cable. I had a junkie one back in 2010 and that caused me some grief.