I have lost a special piece of jewellery and I wanted to know if there where any duas I could make to be reunited with it and why might something just randomly vanish one day

Sometimes we lose something because it’s a trial for us to train ourselves not to be attached to this world and any objects.

To find it, I recommend reading this Du’a:

بِسْمِ اللهِ الرَّحْمٰنِ الرَّحِيْمِ اَصْبَحْتُ فِيْ اَمَانِ اللهِ وَ اَمْسَيْتُ فِيْ جَوَارِ اللهِ.
Transliteration:
BISMIL LAAHIR RAHMAANIR RAHEEM ASBAHTO FEE AMAANIL LAAHE WA AMSAYTO FEE JAWAARIL LAAHE.
Translation:
In the name of Allah, the Beneficent, the Merciful. I have entered upon the morning in the protection of Allah, and I shall enter in to the evening in the refuge of Allah.

If the search is to be made after mid-day the following Dua is to be recited 3 times, clapping each time.

بِسْمِ اللهِ الرَّحْمٰنِ الرَّحِيْمِ اَمْسَيْتُ فِيْ اَمَانِ اللهِ وَ اَصْبَحْتُ فِيْ جَوَارِ اللهِ.
Transliteration:
BISMIL LAAHIR RAHMAANIR RAHEEM AMSAYTO FEE AMAANIL LAAHE WA ASBAHTO FEE JAWAARIL LAAHE.
Translation:
In the name of Allah, the Beneficent, the Merciful. I have entered into the evening in the protection of Allah and I shall enter upon the morning in the refuge of Allah.