replace HR strap or buy new one?

You could try to buy a cheap replacement strap (most Polar-type HRM straps will do, just one thing to look out for: it should not have raised edges around the contacts on the strap. They are ~4 USD on ebay) and cleaning the contact points on the module. If it works without dropouts, noise and spikes you're good. If not, you have wasted the 4 USD.
I hear that the HRM-Run and Tri straps are really good, but personally I didn't get very long term use out of them (worn out 2 in 18 months with daily use) and now I am using an old style 'plastic strap' Garmin HRM-1G for everything except open water swimming, and a HRM-Swim for in the pool. I really like the ease of use and care of the HRM-1G. (For running dynamics I use a RD pod.) But most people prefer the new soft straps, because the wearing comfort is indeed better.

Over time, salt from sweat can build up in the strap, which can sometime provide an easier electrical path for static electricity from some synthetic athletic tops than for the genuine electric signals from the heart. Regular washing of the fabric strap can help dissolve these salts, but over time even washing can fail to completely remove the accumulation.

For such a low cost, I'd suggest a replacement fabric strap, rather than an entirely new HRM.

This is the one I have - Garmin HR-run - Not sure how easy it is to get hold of them now. But if the strap does go, it's not expensive to replace just the strap. I can get one for AUS$45.

Unclip the sensor from the band every time after use to keep the press studs on the sensor from rusting.

Unclip the sensor from the band every time after use to keep the press studs on the sensor from rusting.

I followed this advice faithfully, but could not keep it from rusting—both the strap and pod would rust.

Thanks for all your recommendations. okay i will first try with a new strap. Does anybody have experience with these ebay-noname-straps for <10 bucks or should i stick to the original Garmin ones?

But did you rinse in fresh water after every use?

But did you rinse in fresh water after every use?

Yes...from a water faucet and with mild soap once per week as suggested by Garmin.

Does anybody have experience with these ebay-noname-straps for <10 bucks or should i stick to the original Garmin ones

I work on the principle that you get what you pay for.

I have used those < 10USD straps for years and years with Polar and Garmin HRMs. Hit or miss. Some were great, some were awful. No way to tell in advance, so I used to buy one from 5 or so sellers and then when one or a few of them were good, bought 10 of them -exactly the same ones, same color. It is a lot of hassle for relatively little gain these days, but some years ago it was worth it.

The Garmin straps are an absolute rip off and not worth the money you pay for them. I am now taking a more short term approach and buying cheaper ones from Ebay (£3.50-4.50 each) and now consider these throw away items.

The last one is now seeing 6 months of reliable use, 3-4 times per week.