The class sucks harder than a Warmage (it's like playing 1E, only your spells known reset in under 4 hours for certain ones, meaning you spend half a day learning it and never get to cast it).
It's honestly not that bad, but it's not mindbogglingly awesome. I think you're getting some if its features/problems confused. You keep any spell you retrieve for one hour per sha'ir level no matter what, which is nearly as good as all day after a few levels. You seem to be confusing this with the "time to prepare", which is d4+spell level rounds for a sorc/wiz spell you know, d6+spell level minutes for a sorc/wiz spell you don't know, and d6+spell level hours for
spells that aren't on the sorc/wiz list only. For spells they know they'll prepare faster than a wizard, and for spells they don't "know" it'll take about the same time as a wizard. For divine spells, you might as well not bother. I guess if you have all day and really want Find The Path? Otherwise, ignore their access to divine spells and they're not much worse than other arcane casters in that regard.
It's not clear from the text whether letting a spell expire from your memory actually expends the spell slot for the day, either; "the power to cast the spell dissipates harmlessly" could mean that "the energy of the spell dissipates harmlessly" or "the sha'ir's ability to cast the spell dissipates harmlessly" equally well depending on whether they mean power as energy or power as an ability. The actual Spellcasting ability of the sha'ir refers to a limit on spells cast per day rather than spells retrieved per day, which seems to lean towards not expending the spell if you don't cast it. If it does expend the spell, being a sha'ir will be miserable for the first five levels or so until your spells stick in memory long enough to last out the adventuring day, after which it'll be pretty much like being any other caster unless you get ambushed in the middle of the night. At which point it sucks hard.
Now, all that said, you'll notice I've been saying "okay, it's not much worse than the wizard". Which raises the quite reasonable question: why be at all worse than the wizard when you could be a wizard? Given that their divine spellcasting ability is, as noted, pretty shitty, this is an entirely valid question. I've figured out two reasons you might pick.
First: if you are the kind of guy who leaves spell slots open for the wizard to prep situational spells into, the sha'ir is even better at that than the wizard: he can prep any spell from the sorc/wiz list in less time than a wizard takes to prep it without needing to actually learn the spell. A wizard can theoretically, with enough time and money, accumulate a spellbook with every spell in it; a sha'ir has that spellbook as a class feature. I'm pretty sure this is intended to be the sha'ir's big deal as an advantage, and in the right campaign it's actually a pretty good one.
Second: as magnificently crappy as its divine casting is, the sha'ir is nonetheless both a divine spellcasting class and an arcane spellcasting class. This means it qualifies for and is advanced by divine prestige classes without having to multiclass. You can go sha'ir -> contemplative -> dweomerkeeper without multiclassing or any shenanigans beyond those required to get the necessary K: Religion in the first place. I'm pretty sure this is not actually intended to be an advantage of the sha'ir, but it's better than the actual divine spellcasting itself.
So, yeah. It does have its problems and you'll end up juggling timers a lot. Worse than a warmage? Haha, no.
...oh, yeah, and you have to make a Diplomacy check to prep your spells. Annoying, but we all know how hard it is to get your Diplomacy check decently high, and there's no "cannot take 10" disclaimer.
Edit: Just got bored and checked how long it would take to prep every slot for a level 20 sha'ir at once. Average of 33 minutes if they're known spells. 6 hours 20 or so if none of them are spells from his known list, but if that's the case either you're preparing for some kind of bizarre stunt or you picked absolutely terrible spells known.
Edit 2: Ran some more numbers out of boredom, if you take 5 levels before PrCing out, keep diplomacy maxed and get 5 ranks each of Bluff and Sense Motive it is literally impossible to fail the diplomacy check to get any sorc/wiz spell you are capable of casting with up to two levels of metamagic on it. Spells known get an extra two points of leeway, and this is disregarding Charisma bonus on a Charisma-based caster, so it seems reasonable to say you're just not going to fail the diplomacy check. I would recommend sticking in the class longer than that if the DM rules uncast spells are expended, but if not you'll just need to spend a few minutes re-prepping at worst.