Please add the lines with bb_error_msg (shown as non-indented lines)
in sleep.c in the fragment below:

#if ENABLE_FEATURE_FLOAT_SLEEP

        duration = 0;
        do {
                char *arg = *argv;
                if (strchr(arg, '.')) {
                        double d;
                        char *pp;
                        int len = strspn(arg, "0123456789.");
                        char sv = arg[len];
                        arg[len] = '\0';
                        errno = 0;
                        d = strtod(arg, &pp);
                        if (errno || *pp)
                                bb_show_usage();
                        arg[len] = sv;
                        len--;
                        sv = arg[len];
                        arg[len] = '1';
                        duration += d * xatoul_sfx(&arg[len], sfx);
                        arg[len] = sv;
                } else
                        duration += xatoul_sfx(arg, sfx);
bb_error_msg("arg:%s dur:%f", arg, duration);
        } while (*++argv);

        ts.tv_sec = MAXINT(typeof(ts.tv_sec));
        ts.tv_nsec = 0;
        if (duration >= 0 && duration < ts.tv_sec) {
                ts.tv_sec = duration;
                ts.tv_nsec = (duration - ts.tv_sec) * 1000000000;
        }
bb_error_msg("sec:%u nsec:%u", (unsigned)ts.tv_sec, (unsigned)ts.tv_nsec);
        do {
                errno = 0;
                nanosleep(&ts, &ts);
        } while (errno == EINTR);


recompile, and run "sleep 1". What does it say?

I tested it, and for me it says:

# ./busybox sleep 1
sleep: arg:1 dur:1.000000
sleep: sec:1 nsec:0
[sleeps 1 sec]

# ./busybox sleep 1 2m 3.45
sleep: arg:1 dur:1.000000
sleep: arg:2m dur:121.000000
sleep: arg:3.45 dur:124.450000
sleep: sec:124 nsec:450000000
[sleeps]

Hi Denys,

# sleep 1
sleep: arg:1 dur:0.000000
sleep: sec:0 nsec:0
# sleep 2m 30 0.5 7h
sleep: arg:2m dur:0.000000
sleep: arg:30 dur:0.000000
sleep: arg:0.5 dur:0.000000
sleep: arg:7h dur:0.000000
sleep: sec:0 nsec:0
# 

But, aha! This bit of debug helped me find the problem on my end. The FPU had been removed. Funny that sleep(1) was the only place we noticed it.

I imagine you can now mark this Resolved/WORKSFORME. Thanks for the help.