Been on propranolol 10mg day for a few years for tachycardia and anxiety. If I'm late taking it I get short if breath and my heart pounds hard Normal?

Depends. Depends on what type of arrhythmia you have. Propranolol 10mg is short acting. Needs to be taken 3x/day. You may be experiencing symptoms when it wears off. Lowest dose of long acting pill is 60mg. Also propranolol may worsen asthma symptoms. Consult your primary care doctor to see if you need to increase the dose or stop it altogether and change to a different beta-1 selective blocker. .