I received this desert rose plant as a replacement plant. All the leaves turned brown and dropped off.
There was even a seed pod on the plant that is drying up. Should I cut the long stem to the caudex to see if it produces new leaves or leave it alone?

depending on where you are - will depend on what i suggest ... general location ?

does this plant spend any time out doors ?

the potting media looks * very * dry .... when was the last time the plant was watered ?

I received the plant last monday June 15th and potted it on Tuesday June 16th.
I am in Brooklyn, New York . I watered it when I potted it and it has been indoors. I do not know if I should put it outside. The temp is in the 80's

lets start with the potting mix ....

pull the plant from the pot - mix in added rocks, pumice, pebbles, bark, large grain sand, poultry grit to the soil already in the pot ...this will make a gritty, porous fast draining mix

the faster the water drains from the pot ...the happier your plant will be

place outside if at all possible during the summer months ....

adenium thrive in hot, full sun ....but will die if subjected to freezing temperatures .... the safe low temperature for adenium is 50° ..... whenever temperatures are predicted at or below 50° - it is time to move adenium inside ....

another fatal mistake is letting the pot sit in water ...this will cause root rot

adenium are often associated with being a desert plant ....well, it is ... but as plants, they know only 2 seasons - wet and dry .... with the summer months being the wet season

during the summer months, water like a tropical plant ...in the winter months, treat as if it were a cactus - and barely water at all

outside, with temps in the 80's or so, water thoroughly once every 7 to 10 days or so ...when it warms up into the 90's step up watering to about every 5 days are so

water thoroughly means saturate the plant until water flows from the pot

I wouldn't prune this plant this year .... let it leaf out on its own
once regular watering and the warmth from daily full sun hits the plant ...new leaves will begin to emerge ...and it may even flower

oh yeah ....adenium take forever to respond to any changes .....

I appreciate your help. I used cactus soil that I purchased when I repotted it. I am a little concerned about pulling it out and repotting it. Do you think it will be too much stress to the plant to be repotted again. This will be the third time in two weeks. Also should I remove the drying seed pod?
Thanks.

really needs to re-potted ..... fast draining is almost a requirement for a long lived plant

gather what you need first - bear in mind - if you cant find all that stuff - substitute or leave it out ....

a quick and easy potting tip:
find a small bag of orchid mix, (found at most big box stores) has most of the ingredients i listed ...in fact, its what i used at the start

2 items that i forgot to add is perlite and lump charcoal ....

cut off seed-pod ? ...depends

still a chance you can collect some seed

seed pods mature in about 70 days ..... and they go through all kinds of colors during those 70 days ...from green to purplish to tanish to brownish .....
when seeds pods are about to open, they form a split or crack along its length ...and gradually "peel" themselves back & open sort of like a banana

if there is any "color" left ...leave on plant ...if there is a crack ...leave on plant ..

if dead & dried up ...they might fall off all by themselves

I will try repotting and purchase some orchid mix.