Most of the templates info stored in database on your server.
Here you should download packages to make access to them faster than from remote server.
Please be patient while downloading. TemplateMonster's databse has more than 20000 tempplates and a lot of info describing them.
Data are downloaded rather slow even at ho-speed connections. Biggest packs (Template Screenshots and Template Keywords) can be downloaded up to 15 minuties due to retries and wats.
TM servers are often overloaded so please don't be surprised if you see download errors.
Just retry. The worst that can happen is that you will need to retry few times.