What do you mean by "it won't respond"? How far do you get while making a purchase, and at what point do you get stuck?
eBay has begun sending such "new device" messages for each sign-in from an unrecognized browser. Unrecognized just means that the browser has no cookies from a previous sign-in to that account, or the IP address does not correspond to a previous sign-in.
I do not think there is a way to disable those messages.
If you are routinely erasing your browser cookies, or changing your network address, you can expect to receive such messages when you sign in again.
Do the browser, location and time correspond to your own sign-in activity? If so, you can ignore the message.
Keep in mind that the location may not be precise; it may correspond to the location of the network rather than your actual location. Browser information may not always be available.
If you do not recognize the location, time or browser, and you suspect that someone else may have gained access to your account, you may want to change your eBay password.
