Provided that the Rakshasa Sleeps for More than 1 Hour, He Doesn't
Disguise Self Lasts 1 hour. It needs to be kept up for a Rakshasa to hide its form. Thus, if the Rakshasa is unable to cast Disguise Self at least every hour for any reason, it is unable to hide its form.
Does the Rakshasa Need to Sleep at All?
The Rakshasa is a fiend. While a Rakshasa is not immune to the unconscious condition, there is no rule or piece of fluff that I am aware of indicating that a Rakshasa needs to sleep. They are immune to the Sleep spell via their magic immunity.
That said, skeletons are also not immune to the unconscious condition, and it's fairly obvious that they don't need to sleep. Ditto for Solars, Balors, Empyreans, Ghosts, Golems, etc. I think this is another case of 5e being "rules-light" and relying on the DM to make some common-sense calls. Again, if you rely on the letter of the rules, I think you and your players will be disappointed.
In prior editions (including 3 and 3.5), Rakshasas were outsiders and explicitly did not sleep. So there's that.