Task Killers can free up some memory when you need it, for a short amount of time, but I would disagree with the advice you've been given. You also have to be very careful with them.
In short, Android works very differently to the likes of Windows. Background processes on Android use 0% CPU (and hence 0 power) when idle. If they're not idle, then they're doing something. If they're doing something then they will almost certainly load (or reload) to do whatever it is they want to do.
So... killing off a task unloads it from memory, which uses time, CPU, and lots of power. When it reloads, it'll use more CPU, lots of IO, and more time, so lots more power. Most processes are well behaved, and while they may do something from time to time in the background, the power required to do this is minimal compared to unloading and reloading several times an hour.
Also, many Task Killers are indiscriminate in what they kill off. This may well explain why you're losing connection. It could be killing off a process associated with keeping your connection alive. So killing it kills your connection, and then you waste all that time, CPU, and IO when it reloads a second later to re-establish your connection.
My advice would be to forget about a Task Killer. If you need more memory Android will automatically unload apps that haven't been used in a long time. So for the most part they're just not needed.
If you do decide to keep it, make sure it has some kind of exclude list and add everything to it other than maybe the one or two apps (like ShopSavvy, that loads every couple of hours and tries to get a GPS fix) that really do serve no useful purpose and really do kill your battery.
