TP-Link Modem Router connection problem

[#1]

I have switched my old router (A Thomson one supplied by PlusNet) for a TP Link one as the adapter lead kept breaking off. I have gone through three of these.
Connecting to the internet with my new TP Link TD-W8968 router is a bit hit and miss though. Sometimes I can connect straight away. Other times, I can't connect and the only way to get a connection is by turning it off waiting several seconds and trying again - once or twice.
It's getting a bit annoying. I have tried moving it around in case there is some magnetic interference from a nearby radio and TV but that doesn't work.
Please would you suggest what I could do. Also my broadband usage is not showing up in my account at all for this month even though I have been using the internet every day. I had this occur before with my old router so it looks like it's a recurring problem.

[#2]

It won't be the Modem/Router causing the lack of usage showing UNLESS it is logging into the wrong broadband account. There have been issues with VMBU see http://usertools.plus.net/status/archive/1407766226.htm, go back to the index and the archive if you want to see previous announcements. One of the Customer Relations Team (CRT) may see this tomorrow and check it out for you.
So check the PPP Username and Password are correct and that the connection is set to PPPoA
With the TD-W8968 connecting/not connecting are any lights going out or flashing?
Can you post some DSL line stats with uptime? Can you see what DNS servers it's using?
Could you also check whether it has the latest firmware?
Be very wary of this switching off and on (or rebooting) within a few seconds or the exchange DLM may think you have a dropping connection and slow your speed by raising the Target SNRM or Banding. It would be better to power off for 10 minutes, If you cannot disconnect and reconnect gracefully - which I don't think you can, is there Connect/Disconnect buittons for anything other than the 3g?

[#3]

Many thanks for your detailed and helpful reply.
My modem has been connecting without any problems since my original post. So I haven't looked into yet.
Whenever I have had problems the wifi indicator light and the one to the left of it (in the shape of a globe - is it internet?) have been flashing.
The modem may not have the latest firmware as I just installed it via the installation CD. I will check if there are any updates.
Sorry I'm not very technically minded and I don't know how to get hold of DSK stats. In any case, perhaps it's best to leave those for now as I  don't have any problems again connecting at the moment.
Thanks again for your advice.