A wish keeps the price it was added with unless it's being tracked, and one with no link, no price or a price range is never tracked.
Free tracking also needs Price drop alerts on, and it starts off on new accounts. To turn it on, or to watch any shop with Wishpicks Plus, see "How do I turn on price-drop alerts?".
Steps
Check that Price drop alerts is on in Settings → Notifications.
Open the wish and look under the price. Updated and a time means it's tracked. "Price from" and a date means that price isn't being refreshed, even next to Updates automatically.
No link or price, or a price range? In ⋮ → Edit, add what's missing or switch Price range to Price, then tap Save changes. If it has both and shows only Price from under the price, the shop may have asked not to be tracked.
Seeing "We haven't been able to reach the shop page, so this price may be out of date."? Tap Check the link to open the shop's page. If the product has moved, paste its new link in ⋮ → Edit and tap Save changes.
Otherwise, tap ⋮ → Edit, then Save changes, even with nothing changed: that restarts free tracking. With Wishpicks Plus, if the wish shows Watch this price again, tap it.
Why haven't I had a price-drop email?
Most likely Price drop alerts is off, or the drop was too small to count ("How do I turn on price-drop alerts?" says what counts as a drop). With alerts off there's no email and nothing in Updates, even with Wishpicks Plus.
Tapped "Stop price emails" or "Stop these reminders" in an email? See "How do I choose which emails I get?".
Why did price tracking stop on my wish?
The shop's page kept failing to load (while it's failing, list cards say Price may be stale), nobody opened the wish or its list for a while, or Price drop alerts was turned off. The "Turn off price drop alerts?" message mentions only emails, but turning alerts off stops free tracking too.
Before free tracking lapses, we send a "Keep price tracking on" email: open the list once and tracking carries on. Once it's lapsed, opening won't restart it, but saving the wish in Edit will. Marked it as received, or your Plus ended? See "How do I mark a wish as received?" or "How do I cancel Plus or get a refund?".
Can I fix a wrong price myself?
Yes: tap ⋯ on its card or ⋮ on its page → Edit, change the price and tap Save changes. On a tracked wish (Updated under its price), though, the next check puts the shop's price back unless the shop shows a different currency. If the price it puts back doesn't match the shop's page, tell us in chat with the wish's link: see "How do I contact support?".
Tips
Open your lists every so often: each visit keeps free tracking going.
Keep each wish in the shop's currency: a price in another currency doesn't update.
Can't find a price-drop email? Check Updates: drops land there at the same moment.