Second and subsequent auths with XP supplicant fail

[Viliam Trepak]

The setup:
  AP:
    NICID: id=0x8013 v1.0.0
    PRIID: id=0x0015 v1.1.1
    STAID: id=0x001f v1.8.0
    kernel 2.4.26
    hostap_pci-0.2.2
      ieee_802_1x 1
      ap_bridge_packets 0
      ap_nullfunc_ack 0
      autom_ap_wds 0
      ap_auth_algs 1
      enh_sec 0
      host_encrypt 1
      host_decrypt 1
      bcrx_sta_key 0
      basic_rates 3
      oper_rates 15
      hostapd 1
      hostapd_sta 0
    hostapd-0.2.2
      auth_algs=3	//Open sys or shared key, am I getting it right?
      ieee8021x=1
      wep_key_len_broadcast=13
      wep_key_len_unicast=13
      eapol_key_index_workaround=1  //The same with 0
      no wpa

  Supplicant:
    WinXP with no SP
    EAP-TLS

The symptom:
Start AP, then start XP - all is fine.
Restart XP:
Jun 14 22:38:33 xxx hostapd: wlan0: STA 00:aa:bb:cc:dd:ee IEEE 802.11:
authentication OK (open system)
Jun 14 22:38:33 xxx hostapd: wlan0: STA 00:aa:bb:cc:dd:ee WPA: event 0
notification
Jun 14 22:38:33 xxx hostapd: wlan0: STA 00:aa:bb:cc:dd:ee IEEE 802.11:
did not acknowledge authentication response

Restarting HostAP helps.
Any ideas?