I ride recumbent bikes with very long chains. My experience with them has been that in the reclined seating position, I can put a huge amount of force on the pedals. Sometimes this can be more than the chain can handle, and a link will break.
A lot of bikes use SRAM chains, and SRAM makes quick-closing replacement links called PowerLinks for repairing and allowing quick-disconnect of your chain for cleaning. There are different sizes of PowerLinks depending on if your chain is an eight, nine, or ten speed chain. The PowerLinks are cheap ($5 for a pack of two pairs), so I keep a few pairs in my bike tool bag. It takes around five minutes to repair a broken chain on the road.
To repair a SRAM chain with a PowerLink, you still need a cheap chain rivet remover tool. You remove the broken link with the tool, put one half of the PowerLink on each end of the broken chain, and snap them together. It’s much quicker and more reliable than trying to re-rivet your chain with a chain rivet tool.