I had a similar thing happen this summer and think it's because I overwatered it. I wasn't able to save the plant after it turned brown. Another thought, if the topiary is inside, does it have spider mites? Good luck with your problem; having to start a topiary like that over again isn't fun.

Welll,,,,,,I think it's fun, espec. if you can find a pot of ivy that already has some long stems. I plant a rooted, actively growing ivy,, with more than one stem,,, (about a 3-4"pot size usually) into an 8-10" pot and twine (train) the trailing stems up the wire frame. (Hope you kept it )...Twine half up one side and half up the other..

Pinch the tip ends then,,AND, as they grow new ones to help it fill in -and out. Of course, if you don't and then one day find that some long runners have grown out., pinch the tips and twine them in and around or tuck them in to help the shape and fullness. (or they should be cut off). You'll be pleasantly surprised how fast it will begin to look like you want it to.

If I don't have a plant with multible stems I plant two for faster results.

It's worth a try AND the effort,.. enjoy.. and keep pinching, even after you achieve the shape you want.

P.S.
These sometimes make great gifts. Espec. for those "hard to buy for" folks on your list. AND they'll enjoy them even more when they hear that, YOU GREW IT !!.. And they're usually the right size and color. AND THEY PROBABLY WON'T GET ANOTHER ONE LIKE IT..
BUT,,,,,,,,,,,,,,,,
It would be helpful and polite to give care inltructions along with your creation,, Even if you're sure the receiver already has a few "healthy looking" house plants or it could be on the endangered list as soon as you walk in with it. ..

Basically: Bright indirect light, adaquate drainage ( don't let it sit in a saucer of water after it's taken up all it needs. (( Usually after the bubbles stop)),,, or it's roots will suffocate and then rot.) Water thoroughly,,only when slightly dry, Check for insects ocassionally, espec. before it starts to "look funny" or Puny.. Fertilize according to package directions for house plants.
ALSO,,,,,,,,,
I've found out that it's usually wise to take a clue from their personality and lifestyle, as with any gift, before giving plants or animals. ** They may be allergic.

AND !!!!!
If you've heard them say any of the following,, ""Gosh, I kill everything I touch>>, or,,I must have a brown thumb" I DID say,, "Hard to buy for"........

Happy growing. >>>>>"Aunt" Bren