Here are some tips on locating a break or fault in your invisible fence type system.  First you should visually inspect the area the wire is installed in.  Make a careful and deliberate walk around your perimeter to check for any disturbance of the ground in the area of the wire.  90% of the time the break will be man made from you or someone else digging or otherwise disturbing the area and you can usually find it just by looking.  In my business when I'm called out on a service call to locate a wire break about 50% of the time it could have been located by the owner just by looking.  Do not forget to also check the path of the access pair where it comes from the transmitter out to the perimeter.  There are two wires here and they are either twisted together or laying adjacent. 
If you have ever spliced your system before and not used a grease tube type splice (see http://invincibleservices.com/html/wire__repair_and_splice_kits.html)  then the fault could very well be your old splice going bad so check those first.
If you are still unable to locate the break then you have three choices.
1.  Start digging or pulling up your wire.
2.  Pay for a professional installer to come locate and repair.   ($65 to $125 for service call)
3.  Purchase a wire fault locator to find the break.
If you choose to purchase a locator do not waste your money with the Petsafe or Radio Fence (RFA-50 locator as it is pretty much useless and very difficult to even try to use.  I have recently had a locator designed that functions on the correct RF null principle that is used by the manufacturers of the high end locators that cost $500 or more.  This simple unit costs you  about $85.  Less than the price of a service call.  It is a simplified and far less durable unit but affordable for the DIY person and if you are careful with it it will last you a lifetime.  Contact me through my website or here if you are interested in finding one of these locators.

When you have finally found the break it is important that you use the correct type of splice and there is only one that I have used that will be permanent.  Believe me I have tried everything you could think of and the grease tube is the only one that always works even if it is under 30 feet of water in a lake.  It isn't worth your system failing to try anything else.  When you install a splice you should always have enough extra wire to make sure you tie the ends together with a square knot to avoid the wire being pulled out of the splice.  This usually means inserting a length of wire and actually using 2 splices to fix each break but this is the correct way.  Splice kits can be found on a number of sites including  http://www.invincibleservices.com.  They will cost anywhere from about $8.00 to over $30.00 depending where you buy them and what the shipping charges are and of course how much wire and how many actual splices you need.
Once again if you are unsure of how to do this correctly please contact me with your phone number and I will call and answer all your questions.  Hope this has helped you to keep your dogs safe.

Sincerely,
Dr. Dennis M. Hogan, PhD
www.invincibleservices.com