Restrepias are miniature orchids from the cloud forests of the Andes mountain range in South America, and so require cool moist conditions to thrive. My plants are grown in pure New Zealand sphagnum moss, which most garden centres stock for lining hanging baskets. Don't be tempted to gather moss from hedgerows etc. as this will only contain pests and possibly disease. All my plants are pot grown.
Plastic pots are quite adequate. A 63mm (2.5") pot is ample for the first 2-3 years, and even longer for minute species such as R.aspasicensis and R.howei. I use 76mm (3") square plastic pots for mature plants, and I repot every year with fresh moss, normally in September. This gives the plant a chance to settle before winter. Gently ease the roots from the moss, clean the pot, and wrap the roots in fresh moss. Make sure the 'heart' of the plant is not buried too deep, and the moss is not forced too tight into the pot. You need to allow the moss room to soak up moisture, and to breath. Should the moss start to sprout green shoots, then that's great, just trim it with scissors!
Temperature in my greenhouse is normally around 9-11°C (48-52℉.) during the winter months, and anything up to 29°C (85℉.) on Summer days. The greenhouse is shaded with an Aluminium slatted type fabric. This seems to suit all species of Restrepia. (a 50/60% shade cloth is also fine) A useful guide to good health regarding sunlight is if the leaves have a reddish tinge, then that's good, equally a good green is fine.
Watering is a tricky subject. I can't say that I water once a week as this depends how quickly the moss will dry. What is required is to keep the moss just moist, not wringing wet. These are not aquatic plants! You will definitely kill any Orchid by keeping it wet. I seldom water from the top, as I like to keep my leaves clean and tidy. My plants are held in old garden centre plastic trays which hold 20 plant pots, and have holes in the bottom. So I can lift a tray into a shallow bath of rain water, into which I can put my feed, and 'Slug Clear'. Slugs are my biggest enemy, and lurk in the bottom of the pot, getting in through the drain holes. I don't feed at every watering, usually about every 3rd or 4th, and I use Akerne's RAIN MIX ®. I will leave a tray of plants to soak for about an hour. The excess will soon drain when returned to the bench.
Propagation is done by either division, keiki's, or leaf cuttings. Division needs no explanation, and keiki's are produced naturally on mature leaves on most species. These are best left until a satisfactory root system can be seen. Leaf cuttings are best taken in the spring when plants are making new growth. A mature leaf that has flowered a few times is preferred. Remove the leaf with approx. 40mm of stem. Take off all coverings to show the growth point. Place the cutting in a small pot of clean moss, with the growth point just level with the top of the moss. Rooting should take place in about 6-8 weeks.