Further information:

Using the deadlock finder described here: http://blogs.techrepublic.com.com/datacenter/?p=275

I found that the inserts on the table are blocked by this Full text
query

create table #tmpcatinfo ([ftcatid] smallint,[name] sysname,[path]
nvarchar(260),[status] int,[number_fulltext_tables] int)  if( 1 =
DATABASEPROPERTYEX(db_name(), 'IsFulltextEnabled') )  begin   insert
#tmpcatinfo execute dbo.sp_help_fulltext_catalogs  end        SELECT
cat.name AS [Name], cat.fulltext_catalog_id AS [ID],
CAST(FULLTEXTCATALOGPROPERTY(cat.name,'AccentSensitivity') AS bit) AS
[IsAccentSensitive], CAST(cat.is_default AS bit) AS [IsDefault],
fg.name AS [FileGroup], dp.name AS [Owner],
FULLTEXTCATALOGPROPERTY(cat.name,'LogSize') AS [ErrorLogSize],
FULLTEXTCATALOGPROPERTY(cat.name,'IndexSize') AS [FullTextIndexSize],
FULLTEXTCATALOGPROPERTY(cat.name,'ItemCount') AS [ItemCount],
FULLTEXTCATALOGPROPERTY(cat.name,'UniqueKeyCount') AS
[UniqueKeyCount], FULLTEXTCATALOGPROPERTY(cat.name,'PopulateStatus')
AS [PopulationStatus], 0 AS [PopulationCompletionAge], cast(null as
datetime) AS [PopulationCompletionDate], ci.path AS [RootPath],
CAST(ci.number_fulltext_tables AS bit) AS [HasFullTextIndexedTables],
FULLTEXTCATALOGPROPERTY(cat.name,'PopulateCompletionAge') AS
[PopulationCompletionDateInt],
FULLTEXTCATALOGPROPERTY(cat.name,'PopulateCompletionAge') AS
[PopulationCompletionAgeInt], GETDATE() AS
[PopulationCompletionAgeNow] FROM sys.fulltext_catalogs AS cat LEFT
OUTER JOIN sys.filegroups AS fg ON cat.data_space_id =
fg.data_space_id LEFT OUTER JOIN sys.database_principals AS dp ON
cat.principal_id=dp.principal_id LEFT OUTER JOIN #tmpcatinfo AS ci ON
ci.ftcatid = cat.fulltext_catalog_id WHERE (cat.name=N'myFullText')
drop table #tmpcatinfo

Every time the block occurs sooner.