Why does my still camera stop recording video on its own?
There are three main reasons that still cameras with video functionality have restrictions on the length of video they will shoot.

The first and most common, as tomh pointed out is tax purposes.  The European Union charges a 5% tax on any video recording device and sets the limit at any device capable of recording 30 minutes or more of video.  To avoid this 5% additional fee in the EU, the camera manufacturers limit recording length to 29 minutes and 59 seconds.  Most manufacturers don't bother making a non-EU model, so the rest of the world gets hit with the same limitation.  This reason, however, only applies to cameras with a 29 minute 59 second limit.

The second most common reason is that of file size.  The Fat32 system used by many cameras for the memory card (due to its simplicity and lack of patent encumbrance at this point) is limited to 4GB per single file.  While many cameras are capable of splitting across multiple files, it does involve a few challenges that not all camera manufacturers bother to deal with.  When they don't, it means that the video recording must end when the 4GB file size limit is reached.  This results in a fixed length limit for each quality level, but it will differ based on quality level, with lower video qualities being able to record longer.  You can easily verify if this is the reason by checking the file size of the videos.  Some cameras have third party firmwares and hacks to bypass this limitation, however I'm not aware of any for the Nikon S3300 specifically.

The final reason, which used to be the most common, but is substantially less common with modern cameras, is that of heat.  When CMOS imaging sensors (found in most all modern still cameras) are used, they produce heat.  If the heat can not dissipate fast enough, it eventually results in the sensor overheating, which causes additional noise and eventually sensor damage.  To protect against this, one of two methods can be used.  The oldest is to simply put an arbitrary length limit on recordings that is considered a safe amount of time for the sensor to operate.  Many later systems monitor the temperature of the sensor and only shut down recording when they detect that the sensor is becoming too warm.  It is hard to tell for certain if this is the reason for the recording to be stopping, but in the later case, the time when the recording stops will not be exactly the same between instances, particular when light levels and ambient temperature differ significantly.