Answer: In some special circumstances (described in Help - Foxhound Options - Connection Timeout) the Foxhound Monitor will enter "Connection timeout" state when it can't connect to a target database for about 15 seconds.

After a minute or so (by default, described in Help - Foxhound Options - Timeout Retry), the Foxhound Monitor will try connecting again, and if the special circumstances persist you'll see another "Connection timeout" message, and another, and so on. These messages will appear about 1 minute and 15 seconds apart in Foxhound Options - Display Diagnostics:

1531 2010-04-13 11:10:20.221 Full Build 3659a 1000000003 202a3a(202eh1) Connection timeout for target DSN ... after 19.9s (timeout threshold is 15.0s; see Foxhound Options) - 1000000005
1532 2010-04-13 11:11:35.895 Full Build 3659a 1000000003 202a3a(202eh1) Connection timeout for target DSN ... after 15.2s (timeout threshold is 15.0s; see Foxhound Options) - 1000000046
1533 2010-04-13 11:12:51.696 Full Build 3659a 1000000003 202a3a(202eh1) Connection timeout for target DSN ... after 15.1s (timeout threshold is 15.0s; see Foxhound Options) - 1000000075

See also...
Help - Foxhound Options - Connection Timeout
Help - Foxhound Options - Timeout Retry
How do I see Foxhound diagnostics, errors and exceptions?
Why do I see so many "Timed out" messages on the Monitor display?