Do codes go away?

Stupid question but as I've spent the last 2+ hours going through searches for EVAP and misfire codes...I have a question I couldn't find an answer to.
Let say I have a small evap leak code (PO442 IIRC) and pretend I changed the fuel cap and it fixes it. Would the code go away on its own or will I have to hook it up to a reader and clear it out manually?
I'm getting a small EVAP leak and a misfire on cyl 4 (Po303?). Yup, its an 01 4.0 with auto and so far I haven't seen any indication the head has cracked (yet) but I'm hopeful its not bad. Have to find time to do a compression test on it but I really, REALLY need to get it through the inspection here in VA. Anyone have any advice, thoughts, or cheats? I'd appreciate it.

After X number of "cycles", if there is no repeat of the issue, the code will clear itself.

50 key cycles of no issue and it's gone. For quicker gratification just clear it...

I have seen some CEL codes go away in minutes while driving. They may still lurk as pending codes, with no CEL light for a while longer.

Disconnect for a while the battery if u got no code reAder

Most of the big auto parts retailers (O'Reilly's, Autozone, Advance) will read the codes for you. I would take it to one of these shops and ask them to reset all error codes for you.

thanks guys. Work has had me busier than a 4 butt monkey so the only thing I've been able to do so far was put a new gas cap on and dump in some seafoam. I'll try later this week to hook the code reader at the shop up and see if I can make it go away for good. I'm getting the cyl 3 misfire and the small evap leak. I'll need to chase these issues down so I can get it through inspection. I'm really, REALLY hoping its not one of those pull your hair out exercises.

^^I can say from experience that, at least in NC, they are adamant about NOT clearing codes for you. Apparently it's against the law and the fines are hefty...blah blah.

I had a misfire code related to heat soak that didn't go away after 50+ start-up cycles (yet the problem was fixed), so I just disconnected the battery for a few minutes and reconnected to get rid of the code. Much easier...

They don't clear codes here either, but a friend swears he's gotten the guy to "look the other way" while he pushes the button to reset them...

There is a kind of odd but simple process to clear the codes/memory, if you search for it. You could also (and I recommend this to anyone with an Android device and an OBDII car) buy a Bluetooth OBDII module for about $20, and a $5 app called Torque. Lets you read and clear codes, watch all sorts of sensor data and engine parameters, log data, plot trips, blah blah blah. Maybe the best $25 I've spent on Jeep related junk.

One of the best tools I've ever invested in is a code reader. $99 Actron . There are even effective cheaper ones available...and the phone app ones are reasonably simple and work fairly well. My Jeeps are both Renix and therefore pre-OBD, but my wifes Camry, my Nissan and my Ford Ranger are all OBD II, all my kids cars (4 kids) are OBD II.

Not only can I read, diagnose and clear codes on all these cars, but I get to see my kids more often.

Small evap leak could be the single-walled rubber hose sections between the gray plastic runs between the emissions test pump on the firewall and the charcoal canister back aft.
There is one down low on the firewall driver's side. Another further aft.

Both my '01s had cracking of these hoses a few years ago.
Having a scanner tool has been so important I have one carried in each car. It's an important tool and has helped me make friends at work as I hook up, read and clear co workers error codes