I never had any problems accessing Steemit, and it's still working fine these days.
Steemit uses Cloudflare to protect against DDOS attacks that would overload the site and make it inaccessible for everyone. Do you get a message on multiple high-traffic sites saying that you're blocked? Then Cloudflare probably detected suspicious activity on your IP address. This may have nothing to do with you; maybe another client of the same internet service provider is infected with malware. There are a number of steps you could take to get unblocked, but it's a headache; see https://community.cloudflare.com/t/community-tip-best-practices-for-captcha-challenges/56301
If your internet connection is very slow, it might take a while for the site to load after Cloudflare checks your IP.