You can acquire formulas by reverse-engineering items.
If you fail the crafting check, are you allowed to retry it or are you out of luck?
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"If you fail, you’re left with raw materials and no formula."
No, because there is no item left to reverse engineer anymore. You just have the raw materials.
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If you have an item, you can try to reverse-engineer its formula. This uses the Craft activity and takes the same amount of time as creating the item from a formula would. You must first disassemble the item. After the base downtime, you attempt a Crafting check against the same DC it would take to Craft the item. If you succeed, you Craft the formula at its full Price, and you can keep working to reduce the Price as normal. If you fail, you’re left with raw materials and no formula. If you critically fail, you also waste 10% of the raw materials you’d normally be able to salvage.
You would have to have a second item to disassemble, in order to try again. The first one is gone.
My first impression was the same as yours. Then I read:
The item’s disassembled parts are worth half its Price in raw materials and can’t be reassembled unless you successfully reverse-engineer the formula or acquire the formula another way.
If it had said "reverse-engineered" (referencing the specific attempt) instead of "reverse-engineer" (which sounds like it could allow you to retry until succesful) I wouldn't have hesitated.
If it had said "reverse-engineered" (referencing the specific attempt) instead of "reverse-engineer" (which sounds like it could allow you to retry until succesful) I wouldn't have hesitated.
This changes nothing. You can reverse engineer the formula from another item or "aquire the formula another way".
This also applies to successful reverse engineering attempt, it had to be broad enough to make sure a PC could clearly reassemble the item regardless of how/when they got the formula.