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Yes, it can. A tyre can go flat for a few reasons aside from the more common puncture. These can include:
Low air pressure
One of the more common reasons that a tyre is flat is that the tyre has not properly inflated. This causes the tyre to lose its shape and even make it more prone to damage.
Make sure to check your tyre pressure regularly. If a tyre has lost some air, then top up as required.
Valve problems
A flat tyre could be also be the sign that you have a problem with your valve. Should the valve stem become damaged - through a knock for examples - then air will begin to slowly leak out over time.
Corrosion
Corrosion of the rims or valve stem is another root cause of a flat tyre. If these have begun to rust or corrode then air will escape from the tyre.
Faulty tyre
Sometimes, it can just come down to a tyre being defective. This leads to the tyre losing air even if there is no visible cause or damage.