Summarize data within multiple groups of a time series

One possibility could be:

df %>%
 group_by(birdID, site, rleid = with(rle(site), rep(seq_along(lengths), lengths))) %>%
 summarise(min_ts = min(ts),
           max_ts = max(ts),
           days = difftime(max_ts, min_ts, units = "days")) %>%
 ungroup() %>%
 select(-rleid) %>%
 arrange(birdID, min_ts)

   birdID site  min_ts              max_ts              days           
    <int> <chr> <dttm>              <dttm>              <drtn>         
 1      1 A     2013-04-15 09:29:00 2013-04-22 00:03:00 6.60694444 days
 2      1 B     2013-04-22 14:02:00 2013-04-22 17:02:00 0.12500000 days
 3      1 C     2013-04-22 14:04:00 2013-04-23 00:54:00 0.45138889 days
 4      1 A     2013-04-23 01:20:00 2013-04-30 23:47:00 7.93541667 days
 5      1 B     2013-04-30 03:51:00 2013-04-30 04:26:00 0.02430556 days
 6      2 C     2013-04-30 04:29:00 2013-04-30 18:49:00 0.59722222 days
 7      2 A     2013-05-01 01:03:00 2013-05-02 00:09:00 0.96250000 days
 8      2 C     2013-05-03 07:57:00 2013-05-05 02:54:00 1.78958333 days
 9      2 A     2013-05-05 03:27:00 2013-05-14 00:16:00 8.86736111 days
10      2 D     2013-05-14 10:00:00 2013-05-14 15:00:00 0.20833333 days

Here it creates a rleid()-like grouping variable and then calculates the difference.

Or the same using rleid() from data.table explicitly:

df %>%
 group_by(birdID, site, rleid = rleid(site)) %>%
 summarise(min_ts = min(ts),
           max_ts = max(ts),
           days = difftime(max_ts, min_ts, units = "days")) %>%
 ungroup() %>%
 select(-rleid) %>%
 arrange(birdID, min_ts)