Indissoluble describes things that are really hard to destroy or dissolve and that last a long time, like steel and hard plastic or strong friendships. At five syllables, the word in-dis-sol-u-ble itself even lasts a long time in your mouth.
With roots dating back to the 15th century, indissoluble is a pretty tough adjective — it has survived hundreds of years. You can put a brownie in water and it will dissolve in no time, but a hockey puck in the same water is indissoluble, it won’t dissolve. An expression for indissoluble relationships might be "nothing can tear us apart," because there is so much strength in the bond. A strong law or legal contract also is indissoluble, though the paper it's written on is not.