Give your peas optimal growing conditions, because healthy plants fight disease best. Get a soil test—balanced soil fertility and a pH of 6.5 to 7.0 may prevent root rot. Resist overcrowding your plants (I know it's hard when you have a small space and love peas), because crowded plants are less vigorous. Don't forget that healthy roots need room to grow, so avoid compacting your soil. Throw diseased pea plants away; don't use them as mulch or in compost.
No pea varieties are resistant to root rot. Crop rotation is the most reliable control, so plant a different vegetable in the pea patch if at all possible. Don't use the spot to grow beans (or cover crops of alfalfa, sweet clover, cowpeas, or vetch), because the fungi affect them as well.
One way to rotate crops in a small garden is to plant peas in containers. Fill a large container with sterile potting soil, build a bamboo tepee, and plant peas around the tepee as you would in the garden. If you don't have a lot of space for containers, consider growing the heirloom dwarf pea 'Tom Thumb' (available from Seed Savers Exchange, 563-382-5990, www.seedsavers.org). Its compact growth habit is perfect for smaller-sized pots, and its very frost-hardy.