Other shinigami are always in normal mode, and then when needed, transform into Shikai or Bankai modes. But as soon as Ichigo leaned Bankai mode he never went back to normal mode. Or maybe he is always in normal mode and he always skips Shikai and goes straight into Bankai mode? Why is he different?
According to the Bleach Wiki,
Yoruichi Shihōin has stated that his Zanpakutō is a full-time released form type because of Ichigo's vast but uncontrollable spiritual energy upon generation of it, implying that it is simply a type of Zanpakutō that, without proper control of his spiritual energy, once in Shikai form, remains in said state.
The two characters with constantly released shikai are Ichigo and Zaraki. Both have trait of excessive energy and Zaraki says so openly as explanation for released state of his sword. Which doesn't necessarily mean he is correct about it - he is not into technical side of things.
Since both of them are quite unconventional characters in setting and their abilities are not fully explored, there was no conclusive reason given for it so far.
It is not explained why Ichigo's sword is always in it's released state but many assume it is due to his massive spiritual pressure. although with new information some are considering that it is due to his quincy lineage.
And unlike what Rarst's answer says, Kenpachi Zaraki's sword is not always in its released state. Kenpachi does not have a released state at this point in time is due to the fact that he has never spoken with his zanpakuto. That is just how his swords unreleased state looks just as all soul reaper's have different shaped unreleased zanpakuto. They are all katanas but of different size and shape.
Ichigo is always in shikai mode due to his inability to completely control his massive reiatsu. It is the same with Zaraki, when he openly states that his isn't in its sealed form and that he doesn't even know the name of his zanpakuto, when Ichigo asked him why Zaraki's looked different from everybody else's.
Ichigo cannot seal his sword for a few reasons 1. His seal state was destroyed by byakua 2. He dosent know how 3. His spiritual pressure most probably stops him from doing so
and kempatchi has already stated his sword does not have a sealed state due to his sirritual pressure. It maybe not a full shikai state but it isnt a sealed state possibly closer to how umichicas acts as he can partialy release his shikai
It is not known whether or not Ichigo can reseal his Zanpakuto. However, Zaraki Kenpachi is a different story. Zaraki openly states he never put a seal on his Zanpakuto, opening a new level of discussion. It implies that when Shinigami receive their Zanpakuto they unconsiously put a seal on it which puts it in the common katana state. I could go on typing for days but the short answer is... Tite Kubo probably thinks Ichigo's Shikai looks better that his sealed state.