Softlayer offers this as well. You can spec out a box however you want up to pretty exotic configurations, get billed monthly, and can SSH into them in 3-4 hours.
It is expensive, but not as expensive as something like heroku or aws for equivalent cores/RAM, and you get real hard drives.
We are using Softlayer and we found that on our server we were not bottlenecked by memory, CPU or disk I/O. However, we were bottlenecked by our bandwidth which sat around 5 MB/s. Perhaps we could upgrade to a higher-throughput network card or something (I don't maintain our servers), but we ended up just offloading static files to a CDN instead.
It is expensive, but not as expensive as something like heroku or aws for equivalent cores/RAM, and you get real hard drives.