At least on my Windows machine, the time_sleep_until function appears to calculate the number of microseconds between now and the sleep-until timestamp, and it appears to use unsigned 32-bit math in this calculation. This roundoff leads to a maximum sleep time of just under 4295 seconds (1 hour, 11 minutes, 35 seconds). To get longer sleep times, while still using time_sleep_until to minimize processor overhead, the following loop may be some help to you:
$sleepuntil = strtotime("tuesday 3pm");
while (time() < $sleepuntil)
Of course, one could use something like "cron" instead, to avoid the script doing the extended sleep. Also note that time_nanosleep appears to do similar math, but it is somewhat more intuitive that the seconds parameter has an upper limit on what it can be. Still, both functions might report a warning when waking up prematurely due to roundoff.