There just isn't enough information here for the likes of me to state anything with certainty.
Mifare Classic 1k has a unique ID number and several data sectors which are encoded with keys. A basic duplicator/cloning device might copy the unique ID but not reproduce the data sectors properly without first cracking the associated keys. This is one of many possible explanations for what went wrong with your locksmith duplicate.
Another possibility is the IDTK format which is popular at apartment buildings. This format loops through the bitstream and some duplicators may arbitrarily duplicate bits without the right start/length. The result could be a sequence on the clone which is disjointed when it wraps around.
Unlikely, but maybe this is a dual-frequency fob. If only one format is cloned, the reader could be expecting the other, or even both formats. There are so many more possibilities, I'll stop guessing here.
The most powerful and widely supported tool for identifying, emulating and duplicating RFIDs is the Proxmark 3. Knock-off variants of the "Proxmark3 Easy" can be purchased for less than $40 on sites like AliExpress.
The one thing I am confident of is that your photo is of a passive token. This means RFID/NFC, not an active RF remote that can be sniffed with average SDR. Whatever tools you use will need to be sensitive to near-field electromagnetic energy.