[Xperia Z2 Q&A, Help & Troubleshooting] Einride:
I have the exact same issue and I use a Smartband as well. It seems to be related to wifi on 2.4 GHz only, since I can connect to 5 GHz APs just fine. So BT interference of some sort might be a factor, yes.

Sometimes I'm connected to the AP, the status bar indicator is showing traffic, but I have no internet connection, everything just times out. Other times it takes ages to connect and get an IP from DHCP, before it finally just disconnects from the AP and returns to mobile network.

Checking logcat, there's a constant barrage of errors in wpa_supplicant when this happens:

06-26 12:19:17.435 1326-1326/? I/wpa_supplicant﹕ wlan0: CTRL-EVENT-SCAN-STARTED
06-26 12:19:27.455 1326-1326/? E/wpa_supplicant﹕ wpa_supplicant_ssid_bss_match : wapi is null
06-26 12:19:30.535 1326-1326/? I/wpa_supplicant﹕ wlan0: CTRL-EVENT-SCAN-STARTED
06-26 12:19:40.555 1326-1326/? E/wpa_supplicant﹕ wpa_supplicant_ssid_bss_match : wapi is null
...
06-26 12:30:27.811 1326-1326/? I/wpa_supplicant﹕ wlan0: CTRL-EVENT-SCAN-STARTED
06-26 12:30:37.821 1326-1326/? E/wpa_supplicant﹕ wpa_supplicant_ssid_bss_match : wapi is null

And from dmesg:

<6>[181101.181887] CFG80211-ERROR) wl_cfg80211_add_iw_ie : Previous IW IE is equals to current IE
<6>[181111.211414] CFG80211-ERROR) wl_scan_timeout : timer expired
<6>[181111.211648] CFG80211-ERROR) wl_escan_handler : WLC_E_STATUS_TIMEOUT : scan_request[ef36b300]
<6>[181111.211699] CFG80211-ERROR) wl_escan_handler : escan_on[1], reason[0xffffffff]
<6>[181111.214041] CFG80211-ERROR) wl_escan_handler : escan is not ready ndev f3f96800 wl->escan_on 1 drv_status 0x0 e_type 69 e_states 4
<6>[181161.199815] CFG80211-ERROR) wl_cfg80211_add_iw_ie : Previous IW IE is equals to current IE
<6>[181171.211406] CFG80211-ERROR) wl_scan_timeout : timer expired
<6>[181171.211569] CFG80211-ERROR) wl_escan_handler : WLC_E_STATUS_TIMEOUT : scan_request[ef36bc00]
<6>[181171.211615] CFG80211-ERROR) wl_escan_handler : escan_on[1], reason[0xffffffff]
<6>[181171.213941] CFG80211-ERROR) wl_escan_handler : escan is not ready ndev f3f96800 wl->escan_on 1 drv_status 0x0 e_type 69 e_states 4
<6>[181281.231732] CFG80211-ERROR) wl_cfg80211_add_iw_ie : Previous IW IE is equals to current IE
<6>[181291.251421] CFG80211-ERROR) wl_scan_timeout : timer expired
<6>[181291.251633] CFG80211-ERROR) wl_escan_handler : WLC_E_STATUS_TIMEOUT : scan_request[efcd3900]
<6>[181291.251683] CFG80211-ERROR) wl_escan_handler : escan_on[1], reason[0xffffffff]
<6>[181291.254184] CFG80211-ERROR) wl_escan_handler : escan is not ready ndev f3f96800 wl->escan_on 1 drv_status 0x0 e_type 69 e_states 4
<6>[181401.258382] CFG80211-ERROR) wl_cfg80211_add_iw_ie : Previous IW IE is equals to current IE
<6>[181411.271395] CFG80211-ERROR) wl_scan_timeout : timer expired
<6>[181411.271554] CFG80211-ERROR) wl_escan_handler : WLC_E_STATUS_TIMEOUT : scan_request[ef36b200]
<6>[181411.271604] CFG80211-ERROR) wl_escan_handler : escan_on[1], reason[0xffffffff]
<6>[181411.274855] CFG80211-ERROR) wl_escan_handler : escan is not ready ndev f3f96800 wl->escan_on 1 drv_status 0x0 e_type 69 e_states 4

<6>[182002.187708] CFG80211-ERROR) wl_is_linkdown : Link down Reason : WLC_E_DEAUTH_IND
<6>[182002.187772] link down if wlan0 may call cfg80211_disconnected. event : 6, reason=2 from XX:XX:XX
<6>[182002.194251] CFG80211-ERROR) wl_is_linkdown : Link down Reason : WLC_E_LINK

<6>[182002.207744] cfg80211: Calling CRDA to update world regulatory domain

A Google search for the error message "wapi is null" doesn't turn up much apart from a few others having that issue with the Xperia Z/ZR and in those cases it seems to be an hardware issue (although it seems to be the same person involved in all of those forum and blog posts?). That doesn't bode too well, but on the other hand, I can connect to my 5 GHz wifi AP at home and at work just fine.

I guess I should do a few tests with Bluetooth turned off. I'm pretty sure I wasn't having this issue when I first got this phone (and running SW version .55), although I can't say for certain since I can't remember exactly when this issue popped up.

Update:

Definitely related to Bluetooth in some way. I turned off Bluetooth, rebooted the phone: Wifi connected to the 2.4 GHz AP at work just fine.

Logcat and dmesg with working wifi:

06-26 13:09:43.009 1328-1328/? I/wpa_supplicant﹕ wlan0: CTRL-EVENT-SCAN-STARTED
06-26 13:09:46.539 1328-1328/? E/wpa_supplicant﹕ wpa_supplicant_ssid_bss_match : wapi is null

<6>[ 40.070989] CFG80211-ERROR) wl_cfg80211_add_iw_ie : Previous IW IE is equals to current IE
<6>[ 43.165393] CFG80211-ERROR) wl_cfg80211_connect : Connectting withXX:XX:XX channel (11) ssid "REMOVED", len (13)
<6>[ 50.298294] CFG80211-ERROR) wl_cfg80211_add_iw_ie : Previous IW IE is equals to current IE
<6>[ 118.524346] CFG80211-ERROR) wl_cfg80211_add_iw_ie : Previous IW IE is equals to current IE

OK, so the "wapi is null" and "Previous IW IE" error messages still pop up, even with working wifi. So probably not related.

Then I turned on Bluetooth, Smartband connected, and what do you know? Wifi is now instantly borked again.

Dmesg, the wl_escan errors return:

<6>[ 1310.249870] CFG80211-ERROR) wl_scan_timeout : timer expired
<6>[ 1310.250082] CFG80211-ERROR) wl_escan_handler : WLC_E_STATUS_TIMEOUT : scan_request[f0083500]
<6>[ 1310.250131] CFG80211-ERROR) wl_escan_handler : escan_on[1], reason[0xffffffff]
<6>[ 1310.254431] CFG80211-ERROR) wl_escan_handler : escan is not ready ndev f3b2e800 wl->escan_on 1 drv_status 0x0 e_type 69 e_states 4

I've used the Smartband since the first day I received the phone (since it was bundled with the phone), and I can say with 99.99% certainty that this wasn't an issue to begin with. Unfortunately, I can't remember exactly when this happened first, so it's hard to track down which changes (if any) to the phone causing this. I updated from .55 to .402 at one point (.69 was never released for this phone I think?), and I've unlocked the bootloader while on .402.

There have also been at least two firmware updates for the Smartband since I started using it, no idea if that could cause any issues like this.

Update 2:

I turned off wifi and restarted the phone. When the phone powered up again, with smartband connected, I activated wifi. Now it suddenly works. No "wapi is null" errors in logcat, no wl_scan / wl_escan related dmesg entries. Could be a driver / firmware issue rather than an actual hardware issue, which is a good thing I suppose. Let's see how long it keeps working...