I had issues like yours, but the problem was my router configuration. There are two ways to fix this, one is to change your Wi-Fi settings on the router, the other is to enable QoS (which I understand people sometimes don't like to do) I personally have found doing both solutions works best as these are solutions issued directly by Apple. And in my own experience, this not only fixed connectivity problems, but also speed and stability issues with my Apple devices on my home network.
There are currently two iPhone 4's (not to be confused with iPhone 4S), three iPod touch's (2G, 3G, and 4G {the numerical generations for the iPod's, not the non-existent cellular data connectivity}), an iPad 2, occasionally a MacBook Pro, and three Windows-based PC's (which I am not fond of); speaking simply, if these solutions don't work for you, either you didn't follow the instructions below, or you're simply not someone who should be using such sophisticated devices (A.K.A.-computers, phones, etc....you should probably go be Amish)
➕ Now before I get started, make sure you have WPA2 "Security Mode" enabled with a good password or your neighbors are probably using your Internet. Also the fixes are geared directly towards those with Apple devices who have issues connecting to their own home Wi-Fi, who have WPA2 security enabled on their routers, and also towards those with intermittent connectivity and/or slow connection speeds.
Solution #1
⚠(steps- follow in order or don't bother reading them because you will mess up and whine all over the discussion boards, preventing comp)
1. Go to the router setup page (using your browser, follow the manufacturer's instructions on how to access this)
2. Look for a tab named something like "Applications and Gaming" (and click it)
3. Look for something called QoS (click it)
4. Turn on QoS (which may be called WMM {Wi-Fi multi-media} support depending on the manufacturer of your router)
5. Save your settings by clicking the "Save Settings" button
6. Reboot your router
7. Attempt to connect to your Wi-Fi with your problem device
8. If you are still unable to connect, then continue on to solution #2. If you are able to connect after solution #1, do not screw with your router settings anymore or you will be stuck having to do this all over again.
ℹ-(something that would be somewhat comical due to stupidity, but also a pain in the bum)
Solution #2
⚠(steps- yes you still have to follow them in order, I don't care how smart you think you are, if you want the problem fixed, follow the simple instructions that I am putting 20 minutes of my life into writing for those technologically challenged, or simply hated by their electronics for whatever reason)
1. Go to router setup page
2. Look for a tab named something like "Wireless" (click it)
3. Look for a tab named something like "Basic Wireless Settings" (click it)
4. Now you should see a screen that has stuff like "Network Mode, Network Name, Channel Width, Channel, SSID Broadcast," etc.
5. Look for Network mode (click it and you should see a drop-down menu)
6. If possible, choose "Mixed" as this option provides you with the most compatibility and least amount of headaches. (click mixed and then save your settings by clicking the "Save Settings" button"
7. If you want to be difficult (or are capable of doing this without completely boning your Wi-Fi for every other device) and only use a specific Wi-Fi standard (ex. 802.11a/b/g/n), first verify that the device you are trying to connect supports that wireless standard, and then you must ensure that every other device connecting also supports that standard or you will completely annihilate the ability to connect to your Home Wi-Fi on those devices. (and ensuing the wrath of the owners of those devices until you change the network mode back to 'Mixed")
8. Check the "Channel Width," it should say either "Auto" or "20 MHz Only," and if it doesn't then you need to click it, select "Auto, or 20MHz Only" and click whichever you choose, (personally, I'd just click "Auto"), and save your settings by clicking the "Save Settings" button.
ℹThis is where the ability to see the network and not connect is either your fault for playing with settings you don't understand, or your router manufacturer's fault for telling you to change it (or it being default). Because Apple devices do not support connecting to networks that use 40MHz channel width, besides those that support Wi-Fi (802.11a/b/g/n; 802.11n on 2.4GHz and 5GHz). Many people who have connectivity issues can easily resolve them just by changing this one setting.
9. Reboot your router after saving your settings. (wait 60 seconds to make sure that your changes were saved successfully- usually there is a dialogue that says so unless you are using a cheap router that was built before iPhone's came out)
10. Verify your that your device is able to connect to the network, and if you are able to, then CONGRATULATIONS, YOU NOW MAY USE Wi-Fi ON YOUR DEVICES! If you aren't able to, then you either have an outdated router, or did not follow the instructions.
I hope this guide helped you,
thanks for reading guys!