Are the K-1 losses that were limited by the "At-risk" rules lost?

No. The K-1 disallowed losses due to the At Risk limitation rules are not lost and can be carried over and may be deductible in future years. The term "At risk" means the exposure to the danger of economic loss. A person can claim a tax deduction in a limited partnership up to the amount he or she is at risk if the taxpayer can show it is at risk of never realizing a profit and of losing its initial investment