I've been in Markarth for several days off and on, but no matter what time I get there, Arnleif and Sons are closed. Is this a known bug of some sort? If so, nothing is mentioned on the wiki. What are their normal hours supposed to be? And should I go ahead and open the door (lockpick or console)?

I will admit that ONE evening it was unlocked but they both told me to leave. She didn't have selling in the conversation options, and he doesn't converse just replies. This one time was immediately after starting the Molag Bal quest, around 9-ish, in case that rings any bells.

Have you done the No One Escapes Cidhna Mine quest?
I did that quest pretty early after entering Markarth for the first time so IDK if Markarth is 'normal' before doing that quest. Someone will be along who know for sure.

Sometimes it say it's locked, but it opens like normal. Once you go in and out, it doesn't do it anymore. They should be open from 8:30am to 8:30pm.

I didn't know there was place called Arnleif and Sons in Markarth lol.

I've had this with a few shops in different towns (and houses, as well). Sometimes happens if you turn up at a strange time (like 3am) and there are people on the streets heading for bed. Seems to knock the timings out.

Maybe the proprietor is having... lunch

This has happen to me in windhelm at House of Curiosities I go there round 1 or 2 pm and it closed.

Yes, I've noticed that places will close for lunch now and then too. Guess I'll just open the door and see what happens.

It's like the first door on the right.

Shh...not here...we'll talk inside.

OK, the deal seems to be that around 9-10 at night you can enter and speak to her, comment on the business and get a quest to fetch the last shipment (Dibella statue) she had stolen by the Foresworn. THEN (and only then, apparently) will she finally give the buy/sell conversation option. Guess she's like Fralia Gray-Mane in Whiterun, who also won't buy/sell until you do her missing son quest (but she's there all day calling out that she's selling trinkets "for your fine lady").

I had this, when i walked into the shop ar around 3am it was never the same i rested for 4days and nothing so i reloaded and didnt enter at 3pm (after the attack happend for me) after i did that one thing differently it was all good for me.

also as its scripted to happen at whatever time your there just try to make sure your there enduring the day and then enter anleif and sons, that worked for me too and has been normal ever since.

don't pick the lock it will make it worse