The cage is teeny tiny and much, much to small for a Parrotlet. MUCH to small. They need very large and wide cages. Please order a nice big one when you can. Here is my cage, the dimentions are 21X34 and 36 inches high.
Boredom is a major problem with Parrots. Parrotlets are active and curious. They need many toys, all diff. kinds of swings, perches, rope perches, wood and string toys, etc. Most love bells of all kinds. Coconut toys are big hits. Chipper loves them and loves to eat snacks there.
Toys and a big cage are not an option, they are crutical for the mental and physical health of a parrot. They are intelligent and active and get bored easily. They need playgyms also.
The food must be varied. Not just pellets or seed. Fruit, veggies, sweet potatoes, nutriberries, pasta, brown rice, Beak Appetit, celery, carrots, peas, oatmeal, etc. Muffins and birdie bread full of veggies and fruit are great too. Their diet needs to be varied, just like ours.
You can try bathing more often for the plucking. I give Chipper a bath in the kitchen sink until lukewarm water, barely flowing. Nice and wet. Many people use a mister, but Chipper hates that. It is a good thing to try for most birds. When you get a large cage, add a nice big tub to the outside. Chipper has one and LOVES it. First thing she does when I open her door. She bathes herself.
12 very quiet hours of sleep are also important. Here are some photos of a good size cage, toys and bathtub. They need large toys like the ones in the photos, need a big cage for them.
I think if you do these few things, your birdie will be much happier.