The raising of the face of a guitar is most usually caused by a problem with the soundboard struts.
In some cases the strut doesn't get glued properly during manufacturing and the issue won't show up until after some time under tension.
Occasionally a guitar model is built with a thin top or struts in unconventional locations that causes raising later in the instrument's life.
A sharp knock to the guitar can cause the glue on a strut to break away or the strut to crack, especially a hit on the side of the guitar where the strut end joins the body. The guitar can take a hit and not show any visible body damage. In some cases this can happen during shipping and isn't the fault of the owner.
The glue under the struts can weaken under high temperature, although you won't usually see a problem unless the temperature reaches around 120F / 48C. Higher humidity will make the glue soften at a lower temp. An instrument left in a car or garage, or in its case sitting in the sun in hot parts of the world can reach these temperatures.
Unless your room has extreme conditions of high humidity or heat, it is perfectly safe to leave the instrument out of the case. You might want to get a wall hanger or non-tripod guitar stand though, so there is less risk of the instrument getting knocked off of the bed and taking a hit.
String tension itself should not cause any problems on a standard built guitar made for that type of strings. If there are mechanical problems with the guitar then higher tensions will cause a problem faster than lower tension strings. Putting steel strings on a guitar built for nylon strings will damage the guitar however.