Rumi, student of the great Shamus-i-Tabriz (Sun of Tabriz) is referring to the "dying daily" as it is often referred to. It is the curious task and ability for some (or many) of slipping out of the body and into what is sometimes called the light body as relates to the heavens, universes, and worlds of matter, energy, space, and time -- the worlds of duality -- below the Great Divide. But it can also refer to the movement out of the body in the true form -- Soul Itself -- whose true home is above the forementioned -- above the Great Divide, and where there is not travel at all but simply, being. [by travel one is implying that there exists matter, space and time to 'travel in or around or through'] But when falls into sleep, one is at once out of the body, sometimes manifesting in the form of the dream state, but few are there who know to step into the dream and take over: this is the true dying-daily expressing.
By the statement "You have died many times" he imparts a two-fold meaning: first, that Soul incarnates untold numbers of times; second, that one dies daily when, saying again, one falls into the sleep state, which we are seldom if ever aware of if not trained or been trained to keep of awareness during the sleep state through spiritual exercising, which practice is, say, analogous to one who undertakes daily physical exercising-sets to keep the physical body in condition.
As to the meaning, "remain behind the veil," well, we can suppose this is self-explanatory but in any case has as well a two-fold meaning: first, those who simply are not aware and awakened to the true underpinnings of life as relates to the other worlds except that which orthodoxy and the social engineers espouse and to which people are made to believe and live by and assume as true; second, he conveys of the real and true demarcation between the physical plane and that of the countless other veils and planes that proceed ever-upward, without limit. Because for each plane, there is one above it.
Both these masters (or teachers or coaches) were (and are) just that -- masters, high spiritual masters of the spiritual sciences, and as well artists who knew (and know) well the art of dying daily, who knew to ride the Winds, the heavenly Ethers.