it seems to mean persistent or long-lived. Is that correct...?
Yes, it's correct, but how persistent the effect is is related to the rate of dissociation or rate of turnover of the receptor. It is relative, so to speak; relative to the effect of non-irreversible receptor binding.
Irreversible inhibition of, say, a cell surface receptor means that a drug (agonist/antagonist) binds permanently to the target receptor, usually by binding covalently; the chemical reaction is not reversible. This isn't synonymous with a permanent effect on a cell or organism; that depends on turnover of the receptor. A "faulty" receptor may be replaced quite quickly or not; it depends of the cell and the receptor.
Pseudo-irreversible means that the drug acts in a manner similar to irreversibly bound agonists/antagonists, but there is no covalent bond formed; if a drug/molecule which has a sufficiently high affinity for the receptor is introduced (in a sufficiently high quantity), the new molecule will replace that which was strongly bound before (the pseudo-irreversibly bound drug.)
Some of these types of reactions have been studied more than others. One example of this can be seen with h5-HT7 receptors, which are subject to pseudo-irreversible inactivation by risperidone and 9-OH-risperidone.