Can a pic microcontroller be active all the time everyday?
Most electronic systems can be operated continuously if within their design ratings.
The most common cause of concern is heat.
Unlike say a high computational power desktop/laptop/server/mobile processor, a typical microcontroller doesn't consume more power than it can effectively radiate heat without needing additional cooling design.
Provided that the chip is not misoperated or damaged, and it is not being heated by the environment or other power-hungry components, a typical MCU would be cool or at most warm to the touch.  If the system is rising in temperature, or if it is consuming more powered than specific, then that is a situation which would need concern.
One common reason why an MCU would not be operated 24/7 is if it is in a battery powered design.  But for a mains powered design, a basic MCU may consume little more power than the quiescent current of the mains power supply itself.  It's things like higher performance computers where shutting or slowing them down to reduce mains power consumption makes sense.  A basic flash based MCU with a clock in the double digit MHz can probably keep running as the power used is just not that much, a high end MCU or low end SoC getting into the hundred of MHz and power management makes sense as consumption may approach a watt; by the time you get to say a Raspberry Pi leaving it on all the time without an actual need gets a bit debatable from an energy perspective (though from a thermal perspective is achievable with at most a small fan).