You want to keep it plugged into a monitor for a while and watch out for the undervolt warning (either a lightning bolt or a rainbow in the corner of the screen). Improving the cooling, the quality of the USB cable, and the power supply are also really good ideas.
What have you found so far to be the best options?
In my experience the quality of cabling and power supplies are the factors that most frequently affect stability of electronics hardware.
Make sure the USB port can pump out enough current. Make sure you use a short, thick USB cable. Once you do that, stability issues are gone.
I also put a heat sink on the CPU, but it probably has no effect on stability. It reduces the amount of time the CPU spends in thermal throttling.
The long cables where? I think I know what you're getting at but I would really love some more explanation if possible.
All wires have resistance, and all else being equal, a 2x longer wire will have 2x more resistance. Due to Ohm's law, there is a voltage drop in the cable when you are powering a load (such as the RPi), and this drop will eventually go below the minimum for the load.
Example: the RPi needs 5 volts at 2 amps.
If your cable is 0.1 ohms, then the voltage at the Pi will be 5 - (2 * 0.1) == 4.8 volts.
If your cable is 1 ohms, the voltage at the Pi will be 5 - (2 * 1) == 3 volts.
But because the Pi doesn't always need the full 2 amps, that 1 ohm cable will work sometimes, making debugging harder. Only when you try to do something compute and/or RAM intensive will you notice the board randomly die.
The LED light does go steady red which is an indication that it has conked off and needs a hard reboot
My Pi currently has an uptime of 388 days. I use it as a file-server/backup-machine in my home network. It runs hourly backups for multiple boxes in the background (I use vhpi [0] for this). I have a usb battery attached to it for uninterruptible power supply. It works like a charm. I use NFS over Samba, though.
But I power them off dedicated wall warts.
... and what effect are you implying that this has in this particular context?