Time does not move properly on the island of Blackreef. At the end of each day, the cycle restarts, restoring everything to its original state at the start of the day. Everything, at least.
If you infuse your weapons and abilities with residuum, you can maintain them even after you run out of reprise uses and are sent back to the beginning of the day.
This skill is only obtained after a particular point in the story, namely after defeating Wenjie in The Complex as part of the 'Ubiquity' objective.
Residuum is obtained through interacting with glowing things or defeating Visionaries. If you utilised reprise to rewind your death, you can return to the location where you died to collect residuum.
When you have access to the equipment screen, you can infuse items between each time period. Select 'loadout,' then 'infuse gear,' and then hover over the weapon or ability you want to infuse.
Hold down the 'enter' key to infuse them, which will lock them in for future loops. If you decide you don't want to keep your infused item, you may erase it by clicking on it and then pressing the delete button.
Remember that when you're sent back to the beginning of the loop, you lose all the residuum you're holding, so spend it wisely.