Serial Draw Offers

One of the things I will never understand about correspondence chess is why some opponents continue to offer draws even though earlier offers have been refused. Here's an example from a few years ago.

I had Black and the game started with a Scheveningen Sicilian: 1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 e6 6.Be3 Be7 7.f4 O-O 8.Qf3. Here I realized that with 8...Nc6, we would transpose into the famous Tal - Larsen encounter, game 10 of the Candidates Semifinal, Bled 1965. Although Tal played 9.O-O-O and won, I studied various notes on the game and concluded that Larsen's line was worth a try. After I played 8...Nc6, my opponent might not have recognized the transposition and played 9.Nxc6 instead of 9.O-O-O. I managed to achieve equality after a few more moves.

We eventually reached the position shown in the diagram.

ICCF 1st Webchess Open
Weeks, Mark (2374)

Sanchez Carol, Jesus (2080)
(After 25...Re8-f8)

White played 26.Rxf8+ and offered a draw that I declined with 26... Qxf8. The response was 27.Qxe5 'Draw?', 27...Rxb3 'No!', 28.Qc7 'Draw?', 28...Re3 'No!'. After falling silent for a few moves, my opponent offered another draw, lost a Pawn, repeated the offer, lost a piece, and repeated the offer a last time. A few moves later he resigned.

Here's the PGN game score.

[Event "1st Webchess Open Tournament - Group 16"]
[Site "ICCF-webchess.com"]
[Date "2005.02.01"]
[Round "?"]
[White "Sanchez Carol, Jesus"]
[Black "Weeks, Mark A"]
[Result "0-1"]

1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 e6 6.Be3 Be7 7.f4 O-O 8.Qf3 Nc6 9.Nxc6 bxc6 10.Be2 Qa5 11.O-O Ba6 12.Bxa6 Qxa6 13.Rad1 Rab8 14.b3 d5 15.e5 Nd7 16.Qg3 f6 17.f5 Nxe5 18.fxe6 Rfe8 19.Na4 Qc8 20.Qh3 Rb7 21.c4 dxc4 22.Bd4 cxb3 23.Bxe5 fxe5 24.axb3 Qb8 25.Qh5 Rf8 26.Rxf8+ {Draw?} 26... Qxf8 27.Qxe5 {Draw?} 27...Rxb3 28.Qc7 {Draw?} 28...Re3 29.Qxc6 h6 30.Rf1 Qd8 31. Kh1 Qd3 32.Rg1 {Draw?} 32...Kh7 33.Qc1 Qd4 34.Qc2+ Qe4 35.Qd2 Qxe6 36.Nc5 {Draw?} 36...Qe5 37.Nd7 Re2 38.Qc1 Qe4 39.Qc3 Bd6 40.Qb3 Re1 41.Nf6+ gxf6 42. Qf7+ Kh8 43.Qxf6+ Kg8 44.Qd8+ Bf8 45.h3 Rxg1+ 46.Kxg1 Qe1+ 47.Kh2 Qe5+ 48. g3 a5 49.Qd3 Qe6 50.Qb5 {Draw?} 50...Qa2+ 51.Kg1 a4 52.Qb6 a3 53.Qg6+ Kh8 0-1

What's the point of all the draw offers? Why bother playing in the first place?