A failing shutter is possible, but based on the answers there are simpler things to check first. The most likely issue is autofocus not achieving focus, especially if the camera is set to focus priority. In that mode, the shutter may not fire until focus locks.

Things to check:

• See whether the problem happens only in autofocus modes.
• Try switching to manual focus and see if the shutter releases normally.
• Check whether a front filter is affecting focus.
• Look for a pattern, such as moving from an air-conditioned car into hot, humid air. Slight condensation on the lens or filter can prevent autofocus from locking.

If the camera only refuses to shoot when focus can’t lock, the shutter mechanism may be fine. If it still won’t release even in manual focus and under normal conditions, then a mechanical issue becomes more likely.