RMySQL: LAST_INSERT_ID() always returns 0 - separate connection issue or bug?

Original example as found in some post

According to this post the following SQL statements should give me a vector
1, 2, 2, 2, 2 in the end:

require("RMySQL")
 con <- dbConnect(
     dbDriver("MySQL"),
     db="your_db",
     user="your_user",
     password="your_pw", 
     host="localhost"
 )
 > con
 <MySQLConnection:(6640,122)> 
 > dbSendQuery(con, "DROP TABLE IF EXISTS t;")
 <MySQLResult:(6640,122,0)> 
 > dbSendQuery(con, "CREATE TABLE t (i INT NOT NULL AUTO_INCREMENT PRIMARY KEY);")
 <MySQLResult:(6640,122,1)> 
 > dbSendQuery(con, "INSERT INTO t VALUES(NULL);")
 <MySQLResult:(6640,122,2)> 
 > dbGetQuery(con, "SELECT LAST_INSERT_ID() FROM t;")
   LAST_INSERT_ID()
 1                0
 > dbSendQuery(con, "INSERT INTO t VALUES(NULL),(NULL),(NULL);")
 <MySQLResult:(6640,122,3)> 
 > dbGetQuery(con, "SELECT LAST_INSERT_ID() FROM t;")
   LAST_INSERT_ID()
 1                0
 2                0
 3                0
 4                0
 

Following suggestions by N.B. and Jeff Allen

dbSendQuery(con, "DROP TABLE IF EXISTS t;")
 dbSendQuery(con, paste("CREATE TABLE t", 
     "(i INT NOT NULL AUTO_INCREMENT PRIMARY KEY, x INT);"))
 dbSendQuery(con, "INSERT INTO t SET x=1;")
 > dbGetQuery(con, "SELECT * FROM t;")
   i x
 1 1 1
 > dbGetQuery(con, "SELECT LAST_INSERT_ID();")
   LAST_INSERT_ID()
 1                0
 dbSendQuery(con, "INSERT INTO t SET x=2;")
 > dbGetQuery(con, "SELECT LAST_INSERT_ID();")
   LAST_INSERT_ID()
 1                0
 > dbGetQuery(con, "SELECT * FROM t;")
   i x
 1 1 1
 2 2 2
 

Well, it doesn't, really ;-)

I've googled a bit and AFAIU, LAST_INSERT_ID() is "connection-aware" in the sense that the same connection must be used if it is to work properly. However, I thought that by assigning the connection object to con I was making sure that indeed the same connection is used in each of the statements above.

Well, apparently not ;-) Can anyone help me out with some explanations and/or workarounds?
Using something like select max(<ID>) from <TABLE> isn't going to cut it, though, as I'm running multiple threads that simultaneously write to the DB, thus messing up ID retrieval if done that way.

Thanks!

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