A friend of mine suggested that I leave the cord plugged into the guitar. Removing and inserting the cord daily for practice may damage it and reduce its life. Is it okay that I leave my guitar connected to the amp always and just switch off the amp supply, and turn it back on the next day for practice?
This should not be a problem, although there is no harm in unplugging the instrument. The instrument jacks and the cord are very durable. One danger with leaving it plugged in while you are not holding the guitar is that you might trip over the cord, which could pull on the guitar and knock the guitar off its stand, which might damage the guitar.
Furthermore, players sometimes, while standing up and playing the guitar, accidentally step on the cord and yank it out of the jack on the guitar. That could lead to damaging the cord (and it will make a very unpleasant loud sound through the amplifier).
Here is a YouTube video that shows the correct way to connect the cord to the guitar by looping it through the guitar strap to relieve the tension upon it.
While the quarter inch plug is known to be durable so that frequent unplugging should be ok, it is noteworthy that the pickup's preamp might be switched on and off by the plug. This integrated amp typically runs of a 9-volt battery (or sometimes two of them). Leaving it turned on by not unplugging the cord will therefore result in a faster discharge of the battery and a more frequent need to change it.
Note however that not all electric guitars are active, so check first before troubling yourself.
1) It does no harm to the connector in the guitar, or amp, or the connectors on the cord, to leave them plugged in.
2) If leaving the cord connected bends the cord tightly, curving it with a small radius, the cord itself or the cord-to-connector joint may be damaged. The vast majority of cord failures happen within 300mm/12inches of the end, usually right where the connector body or connector strain-relief ends. When a cord fails, cutting off that last foot or 300mm and re-attaching the connector will often revive it. Unless its been over-bent somewhere other than the ends, or stretched along a large area.
3) If you have battery operated effects boxes, a preamp in the guitar or anything else involving a battery, leaving cords plugged in to that item may leave it switched on, so you'd want to disconnect the cord and save the battery when not using the equipment.
4) Tripping over a connected cord and pulling over the instrument, amp, or both, is a constant danger. On stage or in a practice space, I might leave it connected. If there's foot traffic, disconnect. Be safe, not sorry.