Do all very high heels go a bit wobbly after a while?

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I have a pair of stiletto type high heels (but not crazy high) which I have not worn for a while. They are very good quality italian ones and one of the reasons I bought them was that they felt really comfortable and stable.

Just tried them on tonight after not wearing for a while and they feel a little wobbly - look perfectly ok but I can feel a little wobble. And I promise I haven't been drinking!

Do they usually get like that after a while?

How much have you worn them? I've had this before but only after the shoes had seen a lot of wear.

Reheel and they'll feel like new

Yes, you probably just need to replace the heel tips. They wear out very quickly if you wear them outside.