As I mentioned in my last comment, yesterday I logged into my computer after it had been up for 3 days at the login screen. Upon logging in, polkitd was using nearly 1 GB of memory:

$ uptime
 09:09:38 up 3 days, 15:57, 1 user, load average: 0.06, 0.05, 0.05
$ ps aux | grep polkitd | grep -v grep
root 1034 0.4 11.2 1137788 912732 ? Sl Jul02 23:23 /usr/lib/policykit-1/polkitd --no-debug
$ date
Mon Jul 6 09:11:17 EDT 2015

After nearly 8 hours of being logged in, polkitd memory usage had barely gone up:

$ date; uptime; ps aux | grep polkitd | grep -v grep
Mon Jul  6 17:04:42 EDT 2015
 17:04:42 up 3 days, 23:52,  4 users,  load average: 0.36, 0.25, 0.26
root      1034  0.4 11.2 1148092 913328 ?      Sl   Jul02  23:24 /usr/lib/policykit-1/polkitd --no-debug

Then I added some commands to /etc/rc.local to log polkitd memory usage as well as output from dbus-monitor --system, rebooted my machine, and left it at the login prompt. I checked it this morning, after about 16 hours of being left at the login prompt. The output log from dbus-monitor --system was over 100 MB and nearly entirely full of messages like this, with new messages being constantly added:

signal sender=org.freedesktop.DBus -> dest=(null destination) serial=44 path=/org/freedesktop/DBus; interface=org.freedesktop.DBus; member=NameOwnerChanged
   string ":1.252082"
   string ":1.252082"
   string ""
signal sender=org.freedesktop.DBus -> dest=(null destination) serial=45 path=/org/freedesktop/DBus; interface=org.freedesktop.DBus; member=NameOwnerChanged
   string ":1.252083"
   string ""
   string ":1.252083"
signal sender=org.freedesktop.DBus -> dest=(null destination) serial=46 path=/org/freedesktop/DBus; interface=org.freedesktop.DBus; member=NameOwnerChanged
   string ":1.252083"
   string ":1.252083"
   string ""
signal sender=org.freedesktop.DBus -> dest=(null destination) serial=47 path=/org/freedesktop/DBus; interface=org.freedesktop.DBus; member=NameOwnerChanged
   string ":1.252084"
   string ""
   string ":1.252084"
signal sender=org.freedesktop.DBus -> dest=(null destination) serial=48 path=/org/freedesktop/DBus; interface=org.freedesktop.DBus; member=NameOwnerChanged
   string ":1.252084"
   string ":1.252084"
   string ""

The polkitd memory usage seems to have increased about 10 MB every hour:

Mon Jul  6 17:07:37 EDT 2015
 17:07:37 up 0 min,  0 users,  load average: 2.65, 0.71, 0.24
root      1234  0.0  0.0 279764  7748 ?        Sl   17:07   0:00 /usr/lib/policykit-1/polkitd --no-debug
Mon Jul  6 18:07:38 EDT 2015
 18:07:38 up  1:00,  0 users,  load average: 0.02, 0.02, 0.05
root      1234  0.4  0.2 287188 18908 ?        Sl   17:07   0:16 /usr/lib/policykit-1/polkitd --no-debug
Mon Jul  6 19:07:38 EDT 2015
 19:07:38 up  2:00,  0 users,  load average: 0.03, 0.05, 0.05
root      1234  0.4  0.3 293920 29112 ?        Sl   17:07   0:34 /usr/lib/policykit-1/polkitd --no-debug
Mon Jul  6 20:07:38 EDT 2015
 20:07:38 up  3:00,  0 users,  load average: 0.08, 0.03, 0.05
root      1234  0.4  0.4 300784 39328 ?        Sl   17:07   0:51 /usr/lib/policykit-1/polkitd --no-debug
Mon Jul  6 21:07:38 EDT 2015
 21:07:38 up  4:00,  0 users,  load average: 0.00, 0.01, 0.05
root      1234  0.4  0.6 307516 49816 ?        Sl   17:07   1:09 /usr/lib/policykit-1/polkitd --no-debug
Mon Jul  6 22:07:38 EDT 2015
 22:07:38 up  5:00,  0 users,  load average: 0.00, 0.01, 0.05
root      1234  0.4  0.7 314380 60040 ?        Sl   17:07   1:26 /usr/lib/policykit-1/polkitd --no-debug
Mon Jul  6 23:07:38 EDT 2015
 23:07:38 up  6:00,  0 users,  load average: 0.00, 0.01, 0.05
root      1234  0.4  0.8 321112 70520 ?        Sl   17:07   1:44 /usr/lib/policykit-1/polkitd --no-debug
Tue Jul  7 00:07:38 EDT 2015
 00:07:38 up  7:00,  0 users,  load average: 0.00, 0.02, 0.05
root      1234  0.4  0.9 327976 80756 ?        Sl   Jul06   2:01 /usr/lib/policykit-1/polkitd --no-debug
Tue Jul  7 01:07:38 EDT 2015
 01:07:38 up  8:00,  0 users,  load average: 0.00, 0.03, 0.05
root      1234  0.4  1.1 334708 91244 ?        Sl   Jul06   2:19 /usr/lib/policykit-1/polkitd --no-debug
Tue Jul  7 02:07:38 EDT 2015
 02:07:38 up  9:00,  0 users,  load average: 0.03, 0.04, 0.05
root      1234  0.4  1.2 341440 101472 ?       Sl   Jul06   2:36 /usr/lib/policykit-1/polkitd --no-debug
Tue Jul  7 03:07:38 EDT 2015
 03:07:38 up 10:00,  0 users,  load average: 0.02, 0.05, 0.05
root      1234  0.4  1.3 348304 111700 ?       Sl   Jul06   2:54 /usr/lib/policykit-1/polkitd --no-debug
Tue Jul  7 04:07:38 EDT 2015
 04:07:38 up 11:00,  0 users,  load average: 0.16, 0.06, 0.06
root      1234  0.4  1.5 355036 122176 ?       Sl   Jul06   3:11 /usr/lib/policykit-1/polkitd --no-debug
Tue Jul  7 05:07:38 EDT 2015
 05:07:38 up 12:00,  0 users,  load average: 0.00, 0.01, 0.05
root      1234  0.4  1.6 361900 132400 ?       Sl   Jul06   3:29 /usr/lib/policykit-1/polkitd --no-debug
Tue Jul  7 06:07:38 EDT 2015
 06:07:38 up 13:00,  0 users,  load average: 0.00, 0.01, 0.05
root      1234  0.4  1.7 368632 142876 ?       Sl   Jul06   3:46 /usr/lib/policykit-1/polkitd --no-debug
Tue Jul  7 07:07:38 EDT 2015
 07:07:38 up 14:00,  0 users,  load average: 0.00, 0.01, 0.05
root      1234  0.4  1.8 375496 153096 ?       Sl   Jul06   4:03 /usr/lib/policykit-1/polkitd --no-debug
Tue Jul  7 08:07:38 EDT 2015
 08:07:38 up 15:00,  0 users,  load average: 0.02, 0.26, 0.20
root      1234  0.4  2.0 382228 163312 ?       Sl   Jul06   4:21 /usr/lib/policykit-1/polkitd --no-debug
Tue Jul  7 09:07:38 EDT 2015
 09:07:38 up 16:00,  2 users,  load average: 1.88, 1.94, 0.87
root      1234  0.4  2.1 398868 173812 ?       Sl   Jul06   4:37 /usr/lib/policykit-1/polkitd --no-debug

I'm not sure what those dbus messages mean, so that's the next thing I'll look into.