Thanks for the additional information. It is helpful.
If a urinalysis was not done then there is the possibility that a urinary tract is an issue. Dogs drink about a cup of water for every 8 pounds of body weight each day. You can use that fact to determine if he is drinking more than he requires. Common symptoms of a urinary tract infection are frequent urination, dribbling urine, blood in the urine, squatting frequently to urinate, strong odor to the urine, inappropriate urination and straining to urinate as well as an increase in fluid intake.
A dog with a UTI does not always show all the symptoms and typically displays 2 or 3. I believe you need to have your Vet check your dog out so it can get medication for the problem if your dog is displaying 2 or more of the above symptoms..
Other causes for increased thirst and frequent urination include kidney failure, diabetes mellitus, cushing, and liver disease to name a few. You can read about this here:
Another possible cause is marking behavior. That behavior is harder to correct. Any place he has urinated in the house has to be thoroughly cleaned with a good enzymatic pet odor remover. Be sure to clean up since males do tend to urinate on things and it runs down. The second thing you would need to do is leash him to you and each time he squats or lifts his leg you need to give a short tug to break his concentration and a firm low toned NO. This lets him know urinating inside is unacceptable. Each time he urinated appropriately outside, give him a small treat such as a hot dog sliver. Try to make it a good treat and not a boring normal store bought treat.
I understand your problem with being able to clean up after him, but belly bands absorb the urine and the dog has no repercussion for urinating inside. Normally we suggest crate training in a crate small enough that if the dog urinates in it, they have to sit or lay in it which they don't like. As a result they learn to hold their bladder. When you take them out of the crate, you take them outside and reward them for urinating there. They are allowed a few minutes of free out of crate time (typically 15 minutes) and then back in the crate until the next time. We usually start with 2 hour periods of time for older dogs and extend that to 4 or more hours as they progress through house training. Once they seem to have the message then we allow longer periods of time out of the crate.
Put a bell or other noise maker on the door low enough for the dog to reach. Each time you take the dog out, ring the bell. The dog will associate ringing the bell with going out and one day ring the bell to signal to you that he needs to go out. This will also help as he will be able to tell you if he needs to urinate.
I know that crate training often is a pain for the owner because at the start you have to clean the crate and bathe the dog, but the dog does learn that urinating inside is uncomfortable. I'd compare a belly band to a diaper. Most kids don't mind having a diaper on but urinating in their underwear is uncomfortable so they learn.
Now I did want to mention that beagles are prone to disc issues which can cause issues with a dog knowing that they have to urinate until it is already starting to come out or later. So I do feel I need to mention this as it may be an issue or contributing to the situation. Disc issues can not be ruled out without special imaging. So it is likely to be either a marking or house training issue, but I do want to be thorough and give you the various possibilities.
I hope this information is helpful to you. If you would like any additional information or have more questions please don’t hesitate to press the reply to expert or continue conversation button so I can address any issues you still have . If you do find this helpful, please take this opportunity to rate my answer positively so I am compensated for my time.