Wow, finally someone with my problem - yay, you'll sympathise!
My horse used to respect 'fencing' even if it was a single loose rope. Then I moved him to somewhere with shocking internal fencing & a bully horse cornered him & pushed him thru....
Now, the fences have to be multi strand, tensioned, cattle strength, or at least 2 strand electric to keep him from CLIMBING THROUGH them! He's on 100 acres with mates, no shortage of good grazing... but he likes to explore & has even discovered the one spot on the property, in thick bush, more than half a mile from the other horses(who never get out) where a tree had gone down on the external fence & crossed the MAIN ROAD to visit the neighbours! I wish he was more stupid, I wish he was 'herdbound'!
The only way I've found to contain him without breaking the bank to completely refence is with 2 strand wire electric. I use a car battery & a $30 solar panel to charge it. Tape is not effective enough - wire conducts better & is stronger. The other thing that's important to me, being on an agistment property is that it's portable - with little effort you can set it up anywhere.